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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Review of the Collected Works of John Tate
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by J. S. Milne PDF
Bull. Amer. Math. Soc. 54 (2017), 551-558 Request permission


This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016.
  • Correspondance Serre-Tate. Vol. I, II. Edited, and with notes and commentaries by Pierre Colmez and Jean-Pierre Serre. Documents MathĂ©matiques (Paris), 13, 14. SociĂ©tĂ© MathĂ©matique de France, Paris, 2015.
  • Nicholas M. Katz and John Tate, Bernard Dwork (1923–1998), Notices Amer. Math. Soc. 46 (1999), no. 3, 338–343. MR 1669973
  • Barry Mazur, William Stein, and John Tate, Computation of $p$-adic heights and log convergence, Doc. Math. Extra Vol. (2006), 577–614. MR 2290599
  • Helge Holden and Ragni Piene (eds.), The Abel Prize 2008–2012, Springer, Heidelberg, 2014. MR 3185030, DOI 10.1007/978-3-642-39449-2
  • Jean-Pierre Serre and John Tate, Good reduction of abelian varieties, Ann. of Math. (2) 88 (1968), 492–517. MR 236190, DOI 10.2307/1970722
  • John Tate, Duality theorems in Galois cohomology over number fields, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 288–295. MR 0175892
  • John T. Tate, Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 93–110. MR 0225778
  • J. Tate, The cohomology groups of tori in finite Galois extensions of number fields, Nagoya Math. J. 27 (1966), 709–719. MR 207680, DOI 10.1017/S0027763000026490
  • John Tate, Rigid analytic spaces, Invent. Math. 12 (1971), 257–289. MR 306196, DOI 10.1007/BF01403307
  • John Tate, Symbols in arithmetic, Actes du Congrès International des MathĂ©maticiens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 201–211. MR 0422212
  • John Tate, Galois cohomology, Arithmetic algebraic geometry (Park City, UT, 1999) IAS/Park City Math. Ser., vol. 9, Amer. Math. Soc., Providence, RI, 2001, pp. 465–479. MR 1857470, DOI 10.1090/pcms/009/07
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Additional Information
  • J. S. Milne
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan
  • MR Author ID: 125025
  • Received by editor(s): September 5, 2016
  • Published electronically: June 6, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 54 (2017), 551-558
  • MSC (2010): Primary 01A75, 11-06, 14-06
  • DOI:
  • MathSciNet review: 3683623