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The Life and Work of John Tate

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References

Tate’s Publications

  1. Collected Works of John Tate (B. Mazur and J.-P. Serre edit.), two volumes, Amer. Math. Soc., 2016.

  2. J. Tate, Fourier analysis in number fields and Hecke’s zeta functions, PhD. thesis, Princeton, 1950; in Algebraic Number Theory, Acad. Press (1967), pp.305–347; [CW], no 1.

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  3. E. Artin and J. Tate, Class Field Theory, Princeton, 1951-1952; W A Benjamin, New York, 1990; revised edition, Amer. Math. Soc, Chelsea Publ., 2009.

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  4. J. Tate, The higher dimensional groups of class field theory, Ann. of Math., 56, 1952, pp. 294–297; [CW], no 7.

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  5. 1-, Rational points on elliptic curves over complete fields, unpublished manuscript, Harvard, 1959; reproduced in 1993 in [CW], no 69.

  6. 2-, Duality theorems in Galois cohomology of number fields, in Proc. Internat. Congr. Mathematicians (Stockholm 1962), Inst. Mittag-Leffler, Djursholm (1963), pp.288–295; [CW], no 18.

  7. 3-, Rigid analytic spaces, notes IHES (1962); Invent. math. 12 (1971), pp.257–289; [CW], no 36.

  8. 4-, Formal complex multiplication in local fields (with J. Lubin), Ann. of Math. 81 (1965), pp.380-387; [CW], no 20.

  9. 5-, Algebraic cycles and poles of zeta functions, in Arithmetical Algebraic Geometry, Harper and Row, New York (1965), pp.93–110; [CW], no 21 (completed in [T94]).

  10. 6-, Elliptic curves and formal groups (with J. Lubin and J-P. Serre), unpublished manuscript, reproduced in [CW], no 22.

  11. 7-, Endomorphisms of abelian varieties over finite fields, Invent. math. 2 (1966), pp.134-144; [CW], no 27.

  12. 8-, p-divisible groups, in Proc. Conf. Local Fields (Driebergen 1966), Springer-Verlag (1967), pp.158–163; [CW], no 30.

  13. 9-, Good reduction of abelian varieties (with J-P. Serre), Ann. of Math. 88 (1968), pp.492–517; [CW], no 33.

  14. 10-, Group schemes of prime order (with F. Oort), Ann. Sci. E.N.S. 3 (1970), pp.1–21, [CW], no 34.

  15. 11-, The Milnor ring of a global field (with H. Bass), Lecture Notes in Mathematics 342 (1973), pp.349–446; [CW], no 37.

  16. 12-, Relations between K2 and Galois cohomology, Invent. math. 36 (1976), pp.257–274; [CW], no 45.

  17. 13-, On Stark’s conjecture on the behavior of L(s,x) at s = 0, J. Fac Sci. Univ. Tokyo Math. 28 (1981), pp.963–978; [CW], no 54.

  18. 14-, Les conjectures de Stark sur les fonctions L d’Artin en s = 0 (Lecture notes edited by D. Bernardi and N. Schappacher), Progress in Mathematics 47 (1984), Birkhäuser Boston.

  19. 15-, Refined conjectures of the “Birch and Swinnerton-Dyer type” (with B. Mazur), Duke Math. J. 54 (1987), pp.711–750; [CW], no 59.

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  20. 16-, Some algebras associated to automorphisms of elliptic curves (with M. Artin and M. Van der Bergh), in The Grothendieck Festschrift I, Birkhäuser Boston, 1990, pp.33–85; [CW], no 61.

  21. 17-, Conjectures on algebraic cycles in ℓ-adic cohomology, in Motives Part 1, pp.71–83, A.M.S. (1994); [CW], no 65.

  22. 18-, Autobiography, in [HP] below, pp.249–257.

Other Publications

  1. P Colmez, Tate’s work and the Serre-Tate correspondence, Bull. Amer. Math. Soc. 54 (2017), pp.559–573.

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  2. P. Colmez and J-P. Serre (edit.), Correspondance Serre-Tate, 2 vol., Documents Mathematiques 13–14, Soc Math. France, 2015.

  3. P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, in Modular Functions of One Variable II, L.N. 349, Springer-Verlag 1973, pp.143–316.

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  4. G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkorpern, Invent. math. 73 (1983), pp.349–366; Erratum, ibid. 75 (1984), p. 381.

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  5. 1-, p-adic Hodge theory, J.A.M.S. 1 (1988), pp.255–299.

  6. J-M. Fontaine and W. Messing, p-adic periods and p-adic etale cohomology, A.M.S. Contemp. Math. 67 (1987), pp. 179–207.

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  7. H. Holden and R. Piene (edit), The Abel Prize 2008–2012, Springer-Verlag 2014.

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  8. J.S. Milne, Weil-Châtelet groups over local fields, Ann. Sci. E.N.S. 3 (1970), pp. 273–284.

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  9. -, The work of John Tate, in [HP], pp. 259–334 (contains a detailed analysis and a bibliography of Tate’s publications).

  10. J-P. Serre, Résumé des cours de 1965–1966, in Oeuvres II, pp. 315-324.

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Authors and Affiliations

  1. Collège de France, 6 rue d’Ulm, F-75005, Paris, France

    Jean-Pierre Serre

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  1. Jean-Pierre Serre
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Jean-Pierre Serre, (born September 15,1926, Bages, France), is a French mathematician who was awarded the Fields Medal in 1954. In 2003 he was awarded the first Abel Prize by the Norwegian Academy of Science and Letters. Serre’s mathematical contributions leading up to the Fields Medal were largely in the field of algebraic topology. He was a principal contributor to applications of algebraic geometry to number theory.

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Serre, JP. The Life and Work of John Tate. Reson 25, 169–175 (2020). https://doi.org/10.1007/s12045-020-0934-x

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