Preprints and Publications
Items in each section appear in reverse chronological order. Guide to links: "DOI", "book text", or "journal text" is a published text (contact me for access if needed). "arXiv" is a stable preprint (superseded by a published version when the latter exists) posted on arxiv.org. Other links are self-explanatory (like "pdf" or "errata") or explained in place.
Opinions expressed in my writings need not reflect the views of my institutional affiliates or funding agencies (for more on whom see here).
This file last modified Tuesday, 17-Dec-2024 20:40:00 CST.
Contents
On separate pages:- Overflow (includes dissertation)
- Talks and presentations
Books
| Formats | Title and Citation |
|---|---|
|
second edition: DOI first edition: DOI, pdf, AMS review, errata |
p-adic Differential Equations, second edition
Cambridge Studies in Advanced Mathematics 199, Cambridge Univ. Press, 2022;
first edition,
Cambridge Studies in Advanced Mathematics 125, Cambridge Univ. Press, 2010.
In accordance with my publishing agreement with Cambridge University Press, I have posted a PDF version of the first edition. Please do not redistribute this file! Thank you. |
| DOI |
Perfectoid Spaces
(edited with Debargha Banerjee, Chitrabhanu Chaudhuri, and Ehud de Shalit),
Infosys Science Foundation Series in Mathematical Sciences, Springer, 2022. These are proceedings from a summer school and conference held at ICTS (Bengaluru) in September 2019, including my article Perfectoid spaces: an annotated bibliography. |
| DOI, review | The William Lowell Putnam Mathematical Competition 2001-2016: Problems, Solutions, and Commentary (with Daniel M. Kane, Jonathan M. Kane, and Evan M. O'Dorney), MAA Problem Books, American Mathematical Society, 2020. |
| DOI, my notes (AWS version), my notes (final) | Perfectoid Spaces: Lectures from the 2017 Arizona Winter School (with Bhargav Bhatt, Bryden Cais (ed.), Ana Caraiani, Peter Scholze, and Jared Weinstein), Mathematical Surveys and Monographs 242, American Mathematical Society, 2019. |
| DOI | ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium (edited with Everett W. Howe), Open Book Series 1, Mathematical Sciences Publishers, 2013. |
| DOI, errata |
p-adic Geometry: Lectures from the 2007 Arizona Winter School
(with David Savitt, Dinesh Thakur, Matt Baker, Brian Conrad, Samit Dasgupta, and
Jeremy Teitelbaum), University Lecture Series 45,
American Mathematical Society, 2008.
The original AWS notes are also available at the AWS home page. |
| DOI, errata, amusing photo | The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary (with Bjorn Poonen and Ravi Vakil), Mathematical Association of America (Washington), 2002. |
| website | Geometry Unbound open-source e-book (see website). |
Course notes
Some of these are also available as AMS Open Math Notes.
| Formats | Title |
|---|---|
| html, pdf, repo |
Notes on prismatic cohomology (version of 28 Jun 2023).
These are the edited lecture notes from my topics course from spring 2021. The HTML and PDF versions were generated using PreTeXt. The PreTeXt source is available on GitHub. See also my Math 204B (winter 2021) course page for a series of videos presenting this material. |
| html, PDF, old pdf |
Weil cohomology in practice (version of 22 Jun 2020).
These are the edited lecture notes from my topics course from fall 2019. The HTML and current PDF versions were generated using PreTeXt. The old PDF version is posted at AMS Open Math Notes. |
| html, pdf |
Notes on analytic number theory (version of 28 Oct 2015).
These are the collated (and corrected) notes from my spring 2007 course at MIT. They are also posted at AMS Open Math Notes. I am working on a conversion to PreTeXt; this is the source of the (incomplete) HTML version. |
| html, pdf, repo |
Notes on class field theory (version of 12 Mar 2022).
These are the collated (and corrected) notes from my spring 2002 course at Berkeley. The same version is posted at AMS Open Math Notes. The HTML and PDF versions were generated using PreTeXt. The PreTeXt source is available on GitHub. See also my Math 204B (winter 2021) course page for a series of videos presenting this material. |
Preprints
This section includes work in progress (contact me before reading!), stable preprints, and papers accepted for publication. Not included are the following works in preparation; ask me directly for a status update.
- Frobenius structures on hypergeometric equations, II.
- Title TBA (zeta functions of toric hypersurfaces, with Edgar Costa and David Harvey). In the interim, see Edgar's GitHub repository.
- Title TBA (Relative p-adic Hodge theory, III, with Ruochuan Liu).
- The Robbins phenomenon (with Joe Buhler and Pasha Pylyavskyy).
| Formats | Title (work in progress; unstable) |
|---|---|
| pdf, ipynb |
Abelian varieties over F_2 of prescribed order and dimension (version of 28 Nov 2024). The Jupyter notebook gives computational demonstrations of some of the assertions made in the paper. |
| The relative class number one problem for CM number fields: a status update (version of 17 Dec 2024). | |
| Distribution of Frobenius polynomials of abelian varieties of extremely small order (version of 10 Nov 2024). | |
| pdf, repo | Orbit lookup trees (version of 23 Feb 2024). |
| The de Rham property for representations of products of Galois groups (version of 4 Oct 2023). | |
| F-isocrystals as isoshtukas with no legs (version of 15 Nov 2023). | |
| Vector bundles on products of Fargues-Fontaine curves (version of 10 Mar 2024). |
| Formats | Title (stable preprint) |
|---|---|
| arXiv, repo |
Bounds for the relative class number problem for function fields (with Santiago Arango-Piñeros, María Chara, Asimina Hamakiotes, and Gustavo Rama), arXiv:2412.12467v1 (2024). The Jupyter notebook gives computational demonstrations of some of the assertions made in the paper. |
| arXiv, repo |
A census of genus 6 curves over F_2 (with Yongyuan Huang and Jun Bo Lau), arXiv:2402.00716v1 (2024). The GitHub repository contains associated SageMath and Magma code. The results of this paper have been used to update LMFDB. |
| arXiv | Coleman integration on modular curves (with Mingjie Chen and Jun Bo Lau), arXiv:2401.14513v1 (2024). |
| arXiv | Frobenius sign separation for abelian varieties (with Alina Bucur and Francesc Fité), arXiv:2310.10568v1 (2023), submitted. |
| arXiv | A note on the cohomology of p-adic analytic group actions (with Annie Carter), arXiv:2306.05826v1 (2023). |
| arXiv | Motivic Serre group and Sato-Tate conjecture (with Grzegorz Banaszak), arXiv:2302.13016v1 (2023). |
| arXiv | Monodromy representations of p-adic differential equations in families, arXiv:2209.00593v1 (2022), submitted. |
| arXiv, repo |
The relative class number one problem for function fields, II, arXiv:2206.02084v3 (2024), submitted/in revision. The repository contains Jupyter notebooks documenting the SageMath and Magma computations described in the paper. |
| arXiv | A cut-by-curves criterion for overconvergence of F-isocrystals (with Thomas Grubb and James Upton), arXiv:2202.03604v1 (2022). |
| arXiv, repo, press release, Quanta |
Space vectors forming rational angles (with Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein), arXiv:2011.14232v1 (2020), submitted. The GitHub repository contains C++, Magma, and SageMath code referenced in the paper. The "press release" is a short summary of the results. |
| arXiv |
Étale and crystalline companions, II, arXiv:2008.13053v6 (2023), submitted/in revision.
See also "Notes on isocrystals" and "Étale and crystalline companions, I". |
| Sheafiness criteria for Huber rings (with David Hansen; version of 3 May 2024), submitted/in revision. | |
| arXiv |
Frobenius modules over multivariate Robba rings, arXiv:1311.7468v3 (2020).
This is an updated version of the paper "Some slope theory for multivariate Robba rings". |
| arXiv |
Finiteness of cohomology of local systems on rigid analytic spaces (with Ruochuan Liu),
arXiv:1611.06930v1 (2016). Beware that in the currently posted version, Theorem 0.1(a) is not correct as stated: it should instead read that the cohomology groups are finite-dimensional Banach-Colmez spaces. (This does not affect Theorem 0.1(b).) We are working on an update which will address this issue. |
| arXiv |
Relative p-adic Hodge theory, II: Imperfect period rings (with
Ruochuan Liu), arXiv:1602.06899v3 (2019). We are working on an update to this paper. Contact me for more details. |
|
Rational structures and (phi, Gamma)-modules, draft of
22 Aug 2013. I plan to revise this paper in light of more recent work of Bhatt-Morrow-Scholze (but have not begun to do so). |
Research (mostly) publications
Note that arXiv versions are preprints, and in some cases differ quite significantly from the published versions. To be safe, download (or ask me for) official electronic published versions.
General caution: the older papers in this list (particularly those predating my PhD in 2000) are not very representative of my current mathematical interests, or of topics in which I am willing to review papers.
| Formats | Title and Citation |
|---|---|
| To appear | |
| arXiv, repo |
Hypergeometric L-functions in average polynomial time, II (with Edgar Costa and David Roe), arXiv:2310.06971v3 (2024); to appear in the proceedings of Algorithmic Number Theory Symposium (ANTS-XVI).
We have submitted final page proofs for this article. The SageMath code described in the paper is available from the indicated repository. |
| arXiv, repo |
Sato-Tate groups of abelian threefolds (with Francesc Fité and Andrew V. Sutherland), arXiv:2106.13759v5 (2023), to appear in Memoirs of the American Mathematical Society. The results of this paper have been used to update the L-Functions and Modular Forms Database. See also Drew Sutherland's page of animated examples. |
| 2024 | |
| DOI, arXiv | On the degree of polynomials computing square roots mod p (with Swastik Kopparty), 39th Computational Complexity Conference (CCC 2024), Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, 25:1-25:14. |
| DOI, arXiv, repo |
Geometric decomposition of abelian varieties of order 1 (with Toren D'Nelly-Warady), Research Directions in Number Theory [Women in Numbers 5 proceedings volume] Association for Women in Mathematics Series 33, Springer, Cham, 2024.
The repository contains Jupyter notebooks documenting the SageMath computations described in the paper. |
| DOI, arXiv | Effective Sato-Tate conjecture for abelian varieties and applications (with Alina Bucur and Francesc Fité), Journal of the European Mathematical Society 26 (2024), 1713-1746. |
| DOI, arXiv, ipynb |
Abelian varieties over F_2 of prescribed order,
Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres
(2024), special issue for GTA 2021, 43--58. The Jupyter notebook gives computational demonstrations of some of the assertions made in the paper. |
| DOI, arXiv | Drinfeld's lemma for F-isocrystals, I, International Mathematics Research Notices (2024), article ID rnae039. |
| DOI, arXiv, repo |
The relative class number one problem for function fields, III,
in LuCaNT: LMFDB, Computation, and Number Theory,
Contemporary Mathematics 796, American Mathematical Society, 2024, 55-73.
The volume is the proceedings of the 2023 LuCaNT conference. The repository contains Jupyter notebooks documenting the SageMath and Magma computations described in the paper. |
| DOI, arXiv | Drinfeld's lemma for F-isocrystals, II: Tannakian approach (with Daxin Xu), Compositio Mathematica 160 (2024), 90-119. |
| 2023 | |
| DOI, arXiv | Angle ranks of abelian varieties (with Taylor Dupuy and David Zureick-Brown), Mathematische Annalen (published online 2023). |
| DOI, arXiv | Counterexamples to a conjecture of Ahmadi and Shparlinski (with Taylor Dupuy, David Roe, and Christelle Vincent), Experimental Mathematics 32 (2023), 540-544. |
| 2022 | |
| DOI, arXiv |
Étale and crystalline companions, I, Épijournal de Géométrie Algébrique 6 (2022), article no. 20. This is an offshoot of "Notes on isocrystals" (see below). See also "Étale and crystalline companions, II". |
| DOI, arXiv, repo |
The relative class number one problem for function fields, I, Research in Number Theory 8 (2022), article 79 (proceedings of Algorithmic Number Theory Symposium (ANTS-XV)).
The repository contains Jupyter notebooks documenting the SageMath and Magma computations described in the paper. |
| DOI, arXiv, repo |
Frobenius structures on hypergeometric equations, in
Arithmetic Geometry, Cryptography, and Coding Theory, Contemporary Mathematics 779,
American Mathematical Society, 2022, 135-158. Erratum: in Definition 3.3.1, in the formula for \delta_{A,j}, delete the factor x_j. |
| DOI, arXiv |
Isogeny classes of abelian varieties over finite fields in the LMFDB (with Taylor Dupuy, David Roe, and Christelle Vincent), in Arithmetic Geometry, Number Theory, and Computation,
Simons Symposia, Springer, 2022, 375-448.
The volume is a product of the Simons Collaboration of the same name. |
| DOI, arXiv |
Notes on isocrystals, Journal of Number Theory 237 (2022), 353-394. This article originated from notes to some lectures in the geometric Langlands seminar at Chicago. See also "Étale and crystalline companions, I/II". |
| 2021 | |
| DOI, arXiv | Tamely ramified morphisms of curves and Belyi's theorem in positive characteristic (with Daniel Litt and Jakub Witaszek), International Mathematics Research Notices (2021), article rnab309. |
| DOI, arXiv | Drinfeld's lemma for perfectoid spaces and overconvergence of multivariate (phi, Gamma)-modules (with Annie Carter and Gergely Zábrádi), Documenta Mathematica 26 (2021), 1329-1393. |
| DOI, arXiv | Good formal structures on flat meromorphic connections, III: Irregularity and turning loci, Publications of RIMS 57 (2021), 831-866 (Kashiwara 70th birthday issue). |
| DOI, arXiv | Simple connectivity of Fargues-Fontaine curves, Annales Henri Lebesgue 4 (2021), 1203-1233. |
| DOI, arXiv | Every positive integer is the order of an ordinary abelian variety over F_2 (with Everett W. Howe), Research in Number Theory 7 (2021), article number 59. |
| DOI, arXiv |
Sato-Tate groups of abelian threefolds: a preview of the classification (with Francesc Fité and Andrew V. Sutherland), in
Arithmetic, Geometry, Cryptography and Coding Theory (AGC^2T 2019),
Contemporary Mathematics 770, Amer. Math. Soc., 2021, 103-130. This is an announcement of "Sato-Tate groups of abelian threefolds"; see above. |
| 2020 | |
| DOI, arXiv, repo | Hypergeometric L-functions in average polynomial time (with Edgar Costa and David Roe), in Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), Open Book Series 4, Math. Sci. Pub., Berkeley, 2020, 143-159. |
| DOI, arXiv | Some ring-theoretic properties of A_{inf}, in p-adic Hodge Theory, Simons Symposia, Springer, 2020, 129-141. |
| 2019 | |
| DOI, arXiv, conference version | Mod-2 dihedral Galois representations of prime conductor (with Anna Medvedovsky), in ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium, Mathematical Sciences Publishers, 2019, 325-342. |
| DOI, arXiv, conference version | Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology (with Edgar Costa and David Harvey), in ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium, Mathematical Sciences Publishers, 2019, 221-238. |
| 2018 | |
| DOI, arXiv | On commutative nonarchimedean Banach fields, Documenta Mathematica 23 (2018), 171-188. |
| arXiv, DOI (or try here) |
Automorphisms of perfect power series rings, Journal of Algebra
511 (2018), 358-363.
Errata (from Ofer Gabber): in the proof of Theorem 1, one should first reduce to the case where S is a field (this is needed for the step "Sub'(z) is injective whenever z != 0"). In the last line of the proof, the nonzero value is y_i z_1^{i-1} z_{b_{l+m-d}+1} i p^d. |
| arXiv, volume | On categories of (phi, Gamma)-modules (with Jonathan Pottharst), Algebraic Geometry: Salt Lake City 2015, Part 2, Proceedings of Symposia in Pure Mathematics 97, American Mathematical Society, Providence, 2018, 281-304. |
| DOI, arXiv | Endomorphisms of power series fields and residue fields of Fargues-Fontaine curves (with Michael Temkin), Proceedings of the American Mathematical Society 146 (2018), 489-495. |
| 2017 | |
| DOI, arXiv | Slopes of indecomposable F-isocrystals (with Vladimir Drinfeld), Pure and Applied Mathematics Quarterly 13 (2017), 131-192. |
| DOI, arXiv | Endomorphism fields of abelian varieties (with Bob Guralnick), Research in Number Theory (2017) 3:22. |
| DOI | Bhargava's early work: the genesis of P-orderings (with Paul-Jean Cahen and Jean-Luc Chabert), American Mathematical Monthly 124 (2017), 773-790. |
| arXiv, DOI | On the algebraicity of generalized power series, Beiträge zur Algebra und Geometrie 58 (2017), 499-527. |
| 2016 | |
| arXiv, DOI |
A census of zeta functions of quartic K3 surfaces over F_2 (with Andrew V. Sutherland),
LMS Journal of Computation and Mathematics 19 special issue A (2016), 1-11.
This article is from the proceedings of ANTS-XII, the Twelfth Algorithmic Number Theory Symposium. |
| arXiv, volume | Convergence polygons for connections on nonarchimedean curves, in Nonarchimedean and Tropical Geometry, Simons Symposia, Springer Nature, 2016, 51-98. |
| journal, arXiv | The Hochschild-Serre property for some p-adic analytic group actions, Annales Mathématiques du Québec 40 (2016), 149-157 (Glenn Stevens 60th birthday issue). |
| volume | Sato-Tate groups of some weight 3 motives (with Francesc Fité and Andrew V. Sutherland), in Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, Contemporary Mathematics 663, American Mathematical Society, 2016, 57-101. |
| volume | Motivic Serre group, algebraic Sato-Tate group, and Sato-Tate conjecture (with Grzegorz Banaszak), in Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, Contemporary Mathematics 663, American Mathematical Society, 2016, 11-44. |
| volume | An application of the effective Sato-Tate conjecture (with Alina Bucur), in Frobenius Distributions: Lang-Trotter and Sato-Tate Conjectures, Contemporary Mathematics 663, American Mathematical Society, 2016, 45-56. |
| 2015 | |
| journal |
Reified valuations and adic spectra, Research in Number Theory 1 (2015), 1-42. This paper is quoted in a permanent art installation at UC San Diego. |
| journal, errata | New methods for (phi, Gamma)-modules, Research in the Mathematical Sciences 2:20 (2015) (Robert Coleman memorial issue). |
| DOI, arXiv | Noetherian properties of Fargues-Fontaine curves, International Mathematics Research Notices (2015), article ID rnv227. |
| volume, arXiv |
Sato-Tate groups of genus 2 curves, in Advances on Superelliptic Curves and their Applications, IOS Press, 2015.
These are my lecture notes from the NATO Advanced Study Institute "Arithmetic of Hyperelliptic Curves", held in Ohrid (Macedonia) in August-September 2014. See also the slides from my presentation. |
| journal |
Relative p-adic Hodge theory: Foundations (with Ruochuan Liu),
Astérisque 371 (2015), 239 pages.
Any errata for this paper known at the time "Relative p-adic Hodge theory, II" is updated will be recorded therein; see above. |
| DOI | Almost purity and overconvergent Witt vectors (with Chris Davis), Journal of Algebra 422 (2015), 373-412. |
| DOI | Appendix to: Weil numbers in finite extensions of Q^{ab}: the Loxton-Kedlaya phenomenon (by Florin Stan and Alexandru Zaharescu), Transactions of the American Mathematical Society 367 (2015), 4359-4376. |
| DOI, arXiv | A heuristic for the distribution of point counts for random curves over a finite field (with Jeffrey D. Achter, Daniel Erman, Melanie Matchett Wood, and David Zureick-Brown), Philosophical Transactions of the Royal Society A 373 (2015). |
| DOI errata: DOI | Local and global structure of connections on nonarchimedean curves, Compositio Mathematica 151 (2015), 1096-1156; errata (with Atsushi Shiho), ibid. 153 (2017), 2658-2665. |
| DOI, arXiv |
An algebraic Sato-Tate group and Sato-Tate conjecture (with Grzegorz Banaszak),
Indiana University Mathematics Journal
64 (2015), 245-274. Erratum: in Lemma 6.8, the case of type III should be omitted. The same then goes for Theorem 6.9, Theorem 9.3, and Remark 9.12. |
| 2014 | |
| DOI, erratum | Cohomology of arithmetic families of (phi, Gamma)-modules (with Jonathan Pottharst and Liang Xiao), Journal of the American Mathematical Society 27 (2014), 1043-1115. |
| DOI |
On the Witt vector Frobenius (with Chris Davis),
Proceedings of the American Mathematical Society
142 (2014), 2211-2226.
Errata (from Ofer Gabber): In Definition 3.1, clauses (v) and (v)' should start with "The image of". In the proof of 3.2, from (ix) to (xvi), one cannot directly argue that x_p^p = 1 mod pR unless R is p-torsion-free; instead, use the formula for F in Lemma 1.4(a). |
| 2013 | |
| DOI, journal, arXiv, errata | Nonarchimedean geometry of Witt vectors, Nagoya Mathematical Journal 209 (2013), 111-165. |
| 2012 | |
| arXiv, journal | The probability that a complete intersection is smooth (with Alina Bucur), Journal de Théorie des Nombres de Bordeaux 24 (2012), 541-556. |
| DOI, arXiv, errata | Sato-Tate distributions and Galois endomorphism modules in genus 2 (with Francesc Fité, Víctor Rotger, and Andrew Sutherland), Compositio Mathematica 148 (2012), 1390-1442. |
| arXiv, journal | Effective bounds for Frobenius structures (with Jan Tuitman), Rendiconti del Seminario Matematico della Università di Padova 128 (2012), 7-16. |
| pdf, ipynb, sage |
Effective p-adic cohomology for cyclic cubic threefolds,
in Computational Algebraic and Analytic Geometry, Contemporary Mathematics 572, American Mathematical
Society, 127-171.
These are the notes from a six-lecture series I gave at a summer school on p-adic cohomology, held in Mainz in September-October 2008. The "sage" link is to a Sage worksheet which I used for demonstrations during the lectures; the "ipynb" link is a Jupyter notebook updated for Sage 9.1. |
| DOI, arxiv |
A construction of polynomials with squarefree discriminants,
Proceedings of the American Mathematical Society
140 (2012), 3025-3033. The preprint [4] of Bhargava is subsumed by more recent work of Bhargava, Arul Shankar, and Xiaoheng Jerry Wang. |
| 2011 | |
| journal |
Fast polynomial factorization and modular composition
(with Christopher Umans), SIAM Journal of Computing
40 (2011), 1767-1802 (STOC 2008 special issue).
This is a combined journal version of Umans's STOC 2008 paper "Fast modular composition in small characteristic" and our joint FOCS 2008 paper "Fast modular composition in any characteristic". |
| DOI, arXiv |
Semistable reduction for overconvergent F-isocrystals, IV:
Local semistable reduction at nonmonomial valuations,
Compositio Mathematica 147 (2011), 467-523.
For a correction to this paper, see Remark 4.6.7 of "Local and global structure...". For context, see my page on the semistable reduction project. |
| DOI, arXiv | Swan conductors for p-adic differential modules, II: Global variation, Journal de l'Institut de Mathematiques de Jussieu 10 (2011), 191-224. |
| DOI | Appendix and erratum to Minhyong Kim, "Massey products for elliptic curves of rank 1" (with Jennifer Balakrishnan and Minhyong Kim), Journal of the American Mathematical Society 24 (2011), 281-291. |
| DOI, arXiv, pdf | Good formal structures for flat meromorphic connections, II: Excellent schemes, Journal of the American Mathematical Society 24 (2011), 183-229. |
| 2010 | |
| DOI, arXiv |
On families of (phi, Gamma)-modules (with Ruochuan Liu),
Algebra and Number Theory 4 (2010), 943-967.
The proof of Lemma 6.4 is incorrect (specifically in the second sentence). For a correct argument, see: R. Bellovin, p-adic Hodge theory in rigid analytic families, Algebra and Number Theory 9 (2015), 371-433. |
| DOI, arXiv, erratum: DOI | Good formal structures for flat meromorphic connections, I: Surfaces, Duke Mathematical Journal 154 (2010), 343-418; erratum, ibid. 161 (2012), 733-734. |
| arXiv | Relative p-adic Hodge theory and Rapoport-Zink period domains, in Proceedings of the International Congress of Mathematicians (Hyderabad, 2010), Volume II, Hindustan Book Agency/World Scientific, 2010, 258-279. |
| DOI, arXiv | Explicit Coleman integration for hyperelliptic curves (with Jennifer Balakrishnan and Robert Bradshaw), Algorithmic Number Theory (ANTS-IX), Lecture Notes in Computer Science 6197, Springer-Verlag, 2010, 16-31. |
| DOI, arXiv, erratum: DOI | Differential modules on p-adic polyannuli (with Liang Xiao), Journal de l'Institut de Mathematiques de Jussieu 9 (2010), 155-201; erratum, ibid. 9 (2010), 669-671. |
| 2009 | |
| book text, arXiv, magma |
Bounding Picard numbers of surfaces using p-adic
cohomology (with Timothy G. Abbott and David Roe), in
Arithmetic, Geometry and Coding
Theory (AGCT 2005), Séminaires et Congrès 21,
Societé
Mathématique de France, 2009, 125-159 (text available online).
The "magma" link is to (a tar file of) the Magma implementation described in the final part of the paper. See also Johan de Jong's project. |
| journal text, arXiv |
Some new directions in p-adic Hodge theory,
Journal de Théorie des Nombres de Bordeaux
21 (2009), 285-300.
These are the edited notes from my talk at the conference Journées Arithmétiques in 2007. |
| arXiv, volume | Hyperelliptic curves, L-polynomials, and random matrices (with Andrew Sutherland), in Arithmetic, Geometry, Cryptography, and Coding Theory (AGC^2T 2007), Contemporary Math. 487, Amer. Math. Soc., 2009. |
| DOI, arXiv | Detecting integral polyhedral functions (with Philip Tynan), Confluentes Mathematici 1 (2009), 87-109. |
| arXiv, volume | p-adic cohomology, in D. Abramovich et al. (eds.), Algebraic Geometry: Seattle 2005, Proceedings of Symposia in Pure Math. 80, Amer. Math. Soc., 2009, 667-684. |
| DOI, arXiv | Semistable reduction for overconvergent F-isocrystals, III: local semistable reduction at monomial valuations, Compositio Mathematica 145 (2009), 143-172. |
| arXiv, volume |
Generalizations of product-free subsets (with Xuancheng Shao),
in T. Chow and D. Isaksen (eds.),
Communicating Mathematics,
Contemporary Math. 479, Amer. Math. Soc., 2009, 179-188.
This paper is related to "Product-free subsets of groups, then and now" (see below). |
| arXiv, volume |
Product-free subsets of groups, then and now,
in T. Chow and D. Isaksen (eds.),
Communicating Mathematics,
Contemporary Math. 479, Amer. Math. Soc., 2009, 169-178.
The volume is the proceedings from the conference of the same name in honor of Joe Gallian. |
| DOI, arXiv |
Locally decodable codes from nice subsets of finite fields and
prime factors of Mersenne numbers (with Sergey Yekhanin),
journal version: SICOMP 38 (2009), 1952-1969.
For the conference version, see 2008 publications. |
| 2008 | |
| arXiv, journal, erratum | Slope filtrations for relative Frobenius, Astérisque 319 (2008), 259-301. |
| pdf, conference |
Fast modular composition in any characteristic (with Christopher Umans),
in 49th Annual IEEE Symposium on
Foundations of Computer Science 2008 (FOCS '08), 2008, 146-155.
Invited to the FOCS 2008 special issue of SICOMP. However, it did not appear there because it was combined with an earlier paper by Umans; see "Fast polynomial factorization and modular composition" above. |
| From quadratic reciprocity to class field theory, in
W.T. Gowers (ed.),
The
Princeton Companion to Mathematics,
Princeton Univ. Press, 2008. This is a short expository article on the cited topic. |
|
| arXiv, AMS bookstore, repo, tar, sage |
Search techniques for root-unitary polynomials, in
K.E.Lauter and K.A. Ribet (eds.), Computational Arithmetic
Geometry, Contemporary Math. 463,
Amer. Math. Soc., 2008, 71-82.
The "tar" link is to the original source code provided with the paper (2007); more recent code is available in the GitHub repository under the "repo" link. The "sage" link is even older source code, written jointly with Andre Wibisono. |
| DOI, arXiv |
Locally decodable codes from nice subsets of finite fields and
prime factors of Mersenne numbers (with Sergey Yekhanin),
conference version: Proc. of the 23th IEEE Computational Complexity
Conference (CCC), 2008, 175-186.
For the journal version, see 2009 publications. |
| DOI, arXiv | Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, Compositio Mathematica 144 (2008), 657-672. |
| arXiv, volume |
Computing L-series of hyperelliptic curves (with Andrew
V. Sutherland),
in Algorithmic Number Theory, Springer Lecture Notes in Computer Science 5011,
2008, 312-326. The volume is the proceedings of the ANTS VIII conference. |
| DOI, arXiv, errata | On the geometry of p-typical covers in characteristic p, Canadian Journal of Mathematics 60 (2008), 140-163. |
| 2007 | |
| journal, arXiv | The p-adic local monodromy theorem for fake annuli, Rendiconti del Seminario Mathematico della Università di Padova 118 (2007), 101-146. |
| DOI, arXiv |
Swan conductors for p-adic differential modules, I: A local construction, Algebra and Number Theory
1 (2007), 269-300.
Errata (Liang Xiao): in Hypothesis 2.1.3(b), l must be separable over k. |
|
DOI,
arXiv
erratum: pdf |
Semistable reduction for overconvergent F-isocrystals,
I: Unipotence and logarithmic extensions,
Compositio Mathematica 143 (2007), 1164-1212.
The erratum was pointed out by Atsushi Shiho. |
| DOI, arXiv, tar |
Mass formulas for local Galois representations (with an appendix by Daniel Gulotta),
International Mathematics Research Notices
2007 (2007), article ID rnm021 (25 pages).
The tar file contains the programs referenced in the paper. |
| 2006 | |
| journal text, arXiv | Finite automata and algebraic extensions of function fields, Journal de Théorie des Nombres de Bordeaux 18 (2006), 379-420. |
| DOI, arXiv |
Fourier transforms and p-adic "Weil II",
Compositio Mathematica 142 (2006), 1426-1450.
The published version is somewhat abbreviated from the arXiv version. |
| DOI, arXiv, errata | Finiteness of rigid cohomology with coefficients, Duke Mathematical Journal 134 (2006), 15-97, MR 2239343. |
| DOI, arXiv | Quantum computation of zeta functions of curves, Computational Complexity 15 (2006), 1-19, MR 2226067. |
| 2005 | |
|
journal text,
arXiv
errata: journal text, more errata |
Slope filtrations revisited, Documenta Mathematica 10 (2005), 447-525, MR 2184462; errata, ibid. 12 (2007), 361-362. |
| DOI, arXiv, errata, corrected pdf | Orbits of automorphism groups of fields (with Bjorn Poonen), Journal of Algebra 293 (2005), 167-184, MR 2173971 (2006h:12006). |
| DOI, arXiv, errata | Local monodromy of p-adic differential equations: an overview, International Journal of Number Theory 1 (2005) 109-154, MR 2172335 (2006g:12013). |
| journal text, arXiv, errata | Frobenius modules and de Jong's theorem, Mathematical Research Letters 12 (2005), 303-320, MR 2150886. |
| DOI, arXiv | In search of Robbins stability (with Jim Propp), Advances in Applied Mathematics 34 (2005), 659-668, MR 2128991. |
| journal text, arXiv | More étale covers of affine spaces in positive characteristic, Journal of Algebraic Geometry 14 (2005), 187-192, MR 2092132 (2005h:14035). |
| 2004 | |
| journal text, arXiv |
A p-adic local monodromy theorem, Annals of
Mathematics 160 (2004), 93-184, MR 2119719. The journal version differs significantly from the arXiv version due to a number of late corrections. |
| arXiv, DOI |
Full faithfulness for overconvergent F-isocrystals, in
(refereed proceedings) Adolphson et al (eds.), Geometric
Aspects of Dwork Theory (Volume II), de Gruyter (Berlin),
2004, 819-835, MR 2099088 (2005g:14040). Erratum (Chris Davis and Peter Schneider): page 821, line 10: k should be k((t)). Lemma 6.2: replace "discrete" with "rank 1". Theorem 6.7: the result for O requires K to be discretely valued. |
| DOI, arXiv |
Computing zeta functions via p-adic cohomology, in
Algorithmic Number Theory, Springer Lecture Notes in Computer
Science 3076, 2004, 1-17, MR 2137340.
The volume is the proceedings of the ANTS VI conference. |
| 2003 | |
| journal text, arXiv | Semistable reduction for overconvergent F-isocrystals on a curve, Mathematical Research Letters 10 (2003), 151-159, MR 1981892 (2005e:12010). |
| 2002 | |
| DOI, arXiv |
Étale covers of affine spaces in positive
characteristic, Comptes Rendus de l'Academie des Sciences
de Paris Series I 335 (2002), 921-926, MR 1952550
(2004a:14015). With abbreviated French version. (C'est vrai!) |
| 2001 | |
|
arXiv
errata: pdf |
Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, Journal of the Ramanujan Mathematical Society 16 (2001), 323-338, MR 1877805 (2002m:14019); errata, ibid. 18 (2003), 417-418, MR 2043934 (2005c:14027). |
| DOI |
The algebraic closure of the power series field in positive
characteristic, Proceedings of the American Mathematical
Society 129 (2001), 3461-3470, MR 1860477
(2003a:13025). There is an error in Theorem 8: the statement is only correct when the field K is the algebraic closure of a finite field. However, most of the other results are correct as stated. For further discussion, including a replacement for Theorem 8, see "On the algebraicity of generalized power series". |
| DOI |
Power series and p-adic algebraic closures, Journal
of Number Theory 89 (2001), 324-339, MR 1845241
(2002i:11116). There are errors in Theorems 10 and 11: the statements are only correct when the field K is the algebraic closure of a finite field. The other results are correct as stated. For further discussion, including a replacement for Theorems 10 and 11 (and other errata), see "On the algebraicity of generalized power series". |
| 2000 | |
| DOI | Another combinatorial determinant, Journal of Combinatorial Theory, Series A 90 (2000), 221-223. |
| 1999 | |
| journal text | Continuous functions on compact subsets of local fields (with Manjul Bhargava), Acta Arithmetica 91 (1999), 191-198, MR1735672 (2001d:11117). |
| journal |
A weighted mixed-mean inequality, American Mathematical
Monthly 106 (1999), 355-358. A sequel to "Proof of a mixed arithmetic-mean, geometric-mean inequality" (see below). |
| 1998 | |
| journal | The rook on the half-chessboard, or how not to diagonalize a matrix (with Lenny Ng), American Mathematical Monthly 105 (1998), 900-906, MR 1650874 (99i:15014). |
| DOI, tar |
Solving constrained Pell equations, Mathematics of
Computation 67 (1998), 833-842, MR 1443123
(98g:11147). The tar file contains the Mathematica code described in the paper. |
| journal, erratum |
Product-free subsets of groups,
American Mathematical Monthly 105 (1998),
819-824. This mostly expository article expands upon "Large product-free subsets of finite groups" (see below). |
| 1997 | |
| DOI |
Urn sampling and a majorization inequality, Journal of
Combinatorial Theory Series A 79 (1997), 173-179,
MR 1449756 (97m:05002). From the 1996 Duluth REU. |
| DOI |
Large product-free subsets of finite groups, Journal of
Combinatorial Theory Series A 77 (1997), 339-343,
MR 1429085 (97m:20033). From the 1994 Duluth REU. It seems that a bit of interest in this paper has been generated by a recent paper of Gowers; see also this preprint. |
| 1996 | |
| DOI |
Outerplanar partitions of planar graphs, Journal of
Combinatorial Theory Series B 67 (1996), 238-248,
MR 1399677 (98a:05057). From the 1994 Duluth REU. |
| 1994 | |
| journal | Proof of a mixed arithmetic-mean, geometric-mean inequality, American Mathematical Monthly 101 (1994), 355-357, MR 1270962 (95b:26022). |