[1]
E. Artin and J. Tate, Class Field Theory, AMS Chelsea Publishing, Providence, RI, (2009).
References Bibliography
[2]
C. Breuil, B. Conrad, F. Diamond, and R. Taylor, “On the modularity of elliptic curves over \(\QQ\text{:}\) wild 3-adic exercises”, Journal of the American Mathematical Society 14 (2001), 843--939.
[3]
B. Cais, B. Bhatt, A. Caraiani, K.S. Kedlaya, P. Scholze, and J. Weinstein, Perfectoid Spaces: Lectures from the 2017 Arizona Winter School, American Mathematical Society, (2019).
[4]
J.W.S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, (1967).
[5]
J.-L. Chabert, “From Pólya fields to Pólya groups, I: Galois extensions”, Journal of Number Theory 203 (2019), 360–375.
[6]
C. Chevalley, “La théorie du corps de classes”, Annals of Mathematics 41 (1940), 394–418.
[7]
D. Clausen, “A \(K\)-theoretic approach to Artin maps”, arXiv:1703.07842v2, (2017).
[8]
H. Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer-Verlag, Berlin, (1993).
[9]
H. Cohen, Advanced Topics in Computational Number Theory, Graduate Texts in Mathematics 193, Springer-Verlag, New York, (2000).
[10]
D.A. Cox, Primes of the Form \(x^2 + ny^2\), second edition, John Wiley & Sons, Hoboken, NJ, (2013).
[11]
A. Fröhlich and M.J. Taylor, Algebraic Number Theory, Cambridge University Press, (1991).
[12]
S. Gelbart, Automorphic Forms on Adèle Groups, Annals of Mathematics Studies 83, Princeton University Press, Princeton, NJ, (1975).
[13]
G. Gras, Class Field Theory: From Theory to Practice, Springer Monographs in Mathematics, Springer-Verlag, Berlin, (2003).
[14]
A. Grothendieck, “Sur quelques points d’algèbre homologique”, Tôhoku Mathematical Journal 9 (1957), 119–221.
[15]
A. Grothendieck, “Le groupe de Brauer I, II, III”, in Dix Exposés sur la Cohomologie des Schémas, North-Holland, Amsterdam, (1968).
[16]
W. Grunwald, “Ein allgemeiner Existenzsatz für algebraische Zahlkörper”, Journal für die reine und angewandte Mathematik 169 (1933), 103–107.
[17]
D. Harari, Galois Cohomology and Class Field Theory, Universitext, Springer, Cham, (2020).
[18]
M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, with an appendix by Vladimir G. Berkovich, Annals of Mathematics Studies 151, Princeton University Press, Princeton, NJ, (2001).
[19]
D. Hayes, “A brief introduction to Drinfeld modules”, in The Arithmetic of Function Fields (Columbus, OH, 1991), de Gruyter, Berlin, (1992), 1–32.
[20]
G. Henniart, “Une preuve simple des conjectures de Langlands pour \(\GL(n)\) sur un corps \(p\)-adique”, Inventiones Mathematicae 139 (2000), 439–455.
[21]
D. Hilbert, The Theory of Algebraic Number Fields, Springer-Verlag, Berlin, (1998).
[22]
D.F. Holt, “An interpretation of the cohomology groups \(H_n(G, M)\)”, J. Algebra 60 (1979), no. 2, 307–320.
[23]
I.M. Isaacs, Character Theory of Finite Groups, American Mathematical Society, Providence, RI, (2006).
[24]
N. Jacobson, Basic Algebra, II, W. H. Freeman, San Francisco, (1980).
[25]
G. Janusz, Algebraic Number Fields, American Mathematical Society, (1996).
[26]
F. Jarvis, Algebraic Number Fields, Springer, Cham, (2014).
[27]
A. Kapustin and E. Witten, “Electric-magnetic duality and the geometric Langlands program”, Communications in Number Theory and Physics 1 (2007), 1–236.
[28]
K. Kato, “A generalization of local class field theory by using \(K\)-groups, I”, Proceedings of the Japan Academy, Series A, Mathematical Sciences 53 (1977), 140–143.
[29]
L. Lafforgue, “Chtoucas de Drinfeld et correspondance de Langlands”, Inventiones Mathematicae 147 (2002), 1–241.
[30]
V. Lafforgue, “Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale”, Journal of the American Mathematical Society 31 (2018), 719–891.
[31]
J.C. Lagarias and A.M. Odlyzko, “Effective versions of the Chebotarev density theorem”, in Algebraic Number Fields: L-Functions and Galois Representations, Academic Press, London, (1977), 409–464.
[32]
S. Lang, Algebra, revised third edition, Graduate Texts in Mathematics 211, Springer-Verlag, New York, (2002).
[33]
S. Lang, Algebraic Number Theory, second edition, Graduate Texts in Mathematics 110, Springer-Verlag, New York, (1994).
[34]
G. Laumon and B.C. Ngô, “Le lemme fondamental pour les groupes unitaires”, Annals of Mathematics 168 (2008) 477–573.
[35]
A. Leriche, “About the embedding of a number field in a Pólya field”, Journal of Number Theory 145 (2014), 210–229.
[36]
J. Milne, Class Field Theory, version 4.04,
http://jmilne.org/math/CourseNotes/cft.html.[37]
J. Neukirch, Algebraic Number Theory, Springer-Verlag, Berlin, (1999).
[38]
J. Neukirch, Class Field Theory, the Bonn Lectures, Springer, Heidelberg, (2013).
[39]
N. Nikolov and D. Segal, “On finitely generated profinite groups, I: strong completeness and uniform bounds”, Annals of Mathematics 165 (2007), 171--238.
[40]
E. Noether, “Der Hauptgeschlechtssatz für relativ-galoissche Zahlkörper”, Mathematische Annalen 108 (1933), 411–419.
[41]
B. Poonen, Rational Points on Varieties, Graduate Studies in Mathematics 186, American Mathematical Society, Providence, RI, (2017).
[42]
D. Ramakrishnan and R.J. Valenza, Fourier Analysis on Number Fields, Graduate Texts in Mathematics 186, Springer, New York, (1999).
[43]
P. Scholze, “The local Langlands correspondence for \(\GL_n\) over \(p\)-adic fields”, Inventiones Mathematicae 192 (2013), 663–715.
[44]
J.-P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics 7, Springer-Verlag, New York-Heidelberg, (1973).
[45]
J.-P. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics 42, Springer-Verlag, New York, (1977).
[46]
J.-P. Serre, Local Fields, Graduate Texts in Mathematics 67, Springer-Verlag, New York-Berlin, (1979).
[47]
J.-P. Serre, Algebraic Groups and Class Fields, Graduate Texts in Mathematics 117, Springer-Verlag, New York, (1988).
[48]
J.-P. Serre, Galois Cohomology, corrected reprint of the 1997 English edition, Springer-Verlag, Berlin, (2002).
[49]
J.-P. Serre, Lectures on \(N_X(p)\), CRC Press, Boca Raton, FL, (2012).
[50]
J.-P. Serre, Rational Points on Curves over Finite Fields, with contributions by Everett Howe, Joseph Oesterlé, and Christophe Ritzenthaler, Documents Mathématiques, Société Mathématique de France, (2020).
[51]
J. Silverman, The Arithmetic of Elliptic Curves, second edition, Graduate Texts in Mathematics 106, Springer, Dordrecht, (2009).
[52]
R. Taylor and A. Wiles, “Ring-theoretic properties of certain Hecke algebras”, Annals of Mathematics 141 (1995), 553–572.
[53]
S. Wang, “A counter-example to Grunwald’s theorem”, Annals of Mathematics 49 (1948) 1008–1009.
[54]
J.-L. Waldspurger, “Sur les intégrales orbitales tordues pour les groupes linéaires: un lemme fondamental”, Canadian Journal of Mathematics 43 (1991), 852–896.
[55]
S. Wang, “On Grunwald’s theorem”, Annals of Mathematics 51 (1950), 471–484.
[56]
L. Washington, Introduction to Cyclotomic Fields, second edition, Graduate Texts in Mathematics 83, Springer-Verlag, New York, (1997).
[57]
A. Wiles, “Modular elliptic curves and Fermat’s Last Theorem”, Annals of Mathematics 141 (1995), 443–551.
[58]
H. Zantema, “Integer valued polynomials over a number field”, Manuscripta Mathematica 40 (1982), 155–203.
