no. 11-12
Histoire des mathématiques
La vie et l’oeuvre de John Tate
Serre, Jean-Pierre1
1 Collège de France
Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1129-1133.
Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.125
Serre, Jean-Pierre 1

1 Collège de France 
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Serre, Jean-Pierre. La vie et l’oeuvre de John Tate. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1129-1133. doi : 10.5802/crmath.125. http://www.numdam.org/articles/10.5802/crmath.125/

[1] Artin, Michael; Tate, John; Van den Bergh, Michel Some algebras associated to automorphisms of elliptic curves, The Grothendieck Festschrift (Progress in Mathematics), Volume 86, Birkhäuser, 1990, pp. 33-85 (reproduit dans [4, n°61]) | MR | Zbl

[2] Bass, Hyman; Tate, John The Milnor ring of a global field, Algebraic K-theory II. “Classical” algebraic K-theory, and connections with arithmetic (Lecture Notes in Mathematics), Volume 342, Springer, 1973, pp. 349-446 (reproduit dans [4, n°37]) | MR | Zbl

[3] Lubin, Jonathan; Tate, John Formal complex multiplication in local fields, Ann. Math., Volume 81 (1965), pp. 380-387 (reproduit dans [4, n°20]) | DOI | MR | Zbl

[4] Collected Works of John Tate (Mazur, Barry; Serre, Jean-Pierre, eds.), American Mathematical Society, 2016 (2 vol.)

[5] Mazur, Barry; Tate, John Refined conjectures of the “Birch and Swinnerton–Dyer type”, Duke Math. J., Volume 54 (1987), pp. 711-750 (reproduit dans [4, n°59]) | MR | Zbl

[6] Oort, Frans; Tate, John Group schemes of prime order, Ann. Sci. Éc. Norm. Supér., Volume 3 (1970), pp. 1-21 (reproduit dans [4, n°34]) | Numdam | MR | Zbl

[7] Serre, Jean-Pierre; Tate, John Good reduction of abelian varieties, Ann. Math., Volume 88 (1968), pp. 492-517 (reproduit dans [4, n°33]) | DOI | MR | Zbl

[8] Tate, John Rational points on elliptic curves over complete fields (manuscrit non publié, Harvard, 1959, reproduit dans [4, n°69])

[9] Tate, John The higher dimensional groups of class field theory, Ann. Math., Volume 56 (1952), pp. 294-297 (reproduit dans [4, n°7]) | DOI | MR | Zbl

[10] Tate, John Duality theorems in Galois cohomology over number fields, Proc. Int. Congr. Math. (Stockholm, 1962), Inst. Mittag-Leffler, 1963, pp. 288-295 (reproduit dans [4, n°18]) | Zbl

[11] Tate, John Algebraic cycles and poles of zeta functions, Arithmetical Algebraic Geometry, Harper & Row, 1965, pp. 93-110 (reproduit dans [4, n°21], complété dans [16]) | Zbl

[12] Tate, John Endomorphisms of abelian varieties over finite fields, Invent. Math., Volume 2 (1966), pp. 134-144 (reproduit dans [4, n°27]) | DOI | MR | Zbl

[13] Tate, John Fourier analysis in number fields and Hecke’s zeta functions, Algebraic number theory, Academic Press Inc., 1967 p. 305-347, PhD Thesis, Princeton (USA), 1950, reproduit dans [4, n°1]

[14] Tate, John p-divisible groups, Proc. Conf. Local Fields (Driebergen, 1966), Springer, 1967, pp. 158-163 (reproduit dans [4, n°30]) | DOI | Zbl

[15] Tate, John Rigid analytic spaces, Invent. Math., Volume 12 (1971), pp. 257-289 notes IHES (1962), reproduit dans [4, n°36] | DOI | MR | Zbl

[16] Tate, John Conjectures on algebraic cycles in ℓ-adic cohomology, Motives (Part I) (Proceedings of Symposia in Pure Mathematics), Volume 55, American Mathematical Society, 1994, pp. 71-83 (reproduit dans [4, n°65]) | DOI | MR | Zbl

[17] Tate, John Autobiography, The Abel Prize 2008–2012, Springer, 2014, pp. 249-257 | DOI | Zbl

[18] Colmez, Pierre Tate’s work and the Serre–Tate correspondence, Bull. Am. Math. Soc., Volume 54 (2017) no. 4, pp. 559-573 | DOI | MR | Zbl

[19] Correspondance Serre–Tate (Colmez, Pierre; Serre, Jean-Pierre, eds.), Documents Mathématiques, 13-14, Société Mathématique de France, 2015 (2 vol.) | Zbl

[20] Deligne, Pierre; Rapoport, Michael Les schémas de modules de courbes elliptiques, Modular Functions of One Variable II (Lecture Notes in Mathematics), Volume 349, Springer, 1973, pp. 143-316 | DOI | Zbl

[21] Faltings, Gerd Endlichkeitssäze für abelsche Varietäten über Zahlkörpern, Invent. Math., Volume 73 (1983), pp. 349-366 erratum in ibid. 75 (1984), p. 381 | DOI

[22] Faltings, Gerd p-adic Hodge theory, J. Am. Math. Soc., Volume 1 (1988) no. 1, pp. 255-299 | MR | Zbl

[23] Fontaine, Jean-Marc; Messing, William p-adic periods and p-adic etale cohomology, Current trends in arithmetical algebraic geometry (Contemporary Mathematics), Volume 67, American Mathematical Society, 1987, pp. 179-207 | DOI | Zbl

[24] Milne, James S. Weil–Châtelet groups over local fields, Ann. Sci. Éc. Norm. Supér., Volume 3 (1970), pp. 273-284 | DOI | Numdam | Zbl

[25] Milne, James S. The work of Tate, John, The Abel Prize 2008–2012, Springer, 2014, pp. 259-334 (contient une analyse détaillée et une bibliographie des publications de Tate) | DOI | Zbl

[26] Serre, Jean-Pierre Résumé des cours de 1965–1966, Oeuvres II, 1965, pp. 315-324

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