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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 "arXiv" is a stable preprint (superseded by a published version when the latter exists) posted on arxiv.org.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 Monday, 18-Mar-2024 12:52:43 CDT.

Contents

On separate pages:

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 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.

Formats Title (work in progress; unstable)
pdf, repo Orbit lookup trees (version of 23 Feb 2024).
pdf The de Rham property for representations of products of Galois groups (version of 4 Oct 2023).
pdf F-isocrystals as isoshtukas with no legs (version of 15 Nov 2023).
pdf Vector bundles on products of Fargues-Fontaine curves (version of 10 Mar 2024).

    • Formats Title (stable preprint)
    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), submitted.
    arXiv On the degree of polynomials computing square roots mod p (with Swastik Kopparty), arXiv:2311.10956v2 (2024).
    arXiv Frobenius sign separation for abelian varieties (with Alina Bucur and Francesc Fité), arXiv:2310.10568v1 (2023), submitted.
    arXiv, repo Hypergeometric L-functions in average polynomial time, II (with Edgar Costa and David Roe), arXiv:2310.06971v2 (2024), submitted.
    The SageMath code described in the paper is available from the indicated repository.
    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:2206.02084v2 (2023), submitted.
    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".
    pdf Sheafiness criteria for Huber rings (with David Hansen; version of 23 Feb 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.
    pdf 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
    DOI, arXiv Drinfeld's lemma for F-isocrystals, I, International Mathematics Research Notices (2024), article ID rnae039.
    arXiv Effective Sato-Tate conjecture for abelian varieties and applications (with Alina Bucur and Francesc Fité), arXiv:2002.08807v2 (2023); to appear in Journal of the European Mathematical Society.
    We have submitted final page proofs for this article.
    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.
    arXiv, repo Geometric decomposition of abelian varieties of order 1 (with Toren D'Nelly-Warady), arXiv:2109.03986v2 (2022); to appear in the Women in Numbers 5 proceedings volume.
    We have submitted final page proofs for this article. The repository contains Jupyter notebooks documenting the SageMath computations described in the paper.
    arXiv, ipynb Abelian varieties over F_2 of prescribed order, arXiv:2107.12453v3 (2022), to appear in Publications Mathématiques de Besançon (special issue for GTA 2021).
    I have submitted final page proofs for this article. The Jupyter notebook gives computational demonstrations of some of the assertions made in the paper.
    2024
    volume, 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.
    I have submitted final page proofs for this article. 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.
    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.
    pdf 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).