John Tate

John Tate

John Torrence Tate Jr., born March 13, 1925 in Minneapolis, Minnesota, is an American mathematician, distinguished for many fundamental contributions in algebraic number theory and related areas in algebraic geometry. He wrote a Ph.D. at Princeton in 1950 as a student of Emil Artin, was at Harvard University 1954-1990, and is now at the University of Texas at Austin.

Tate's thesis, on the analytic properties of the class of L-functions introduced by Erich Hecke, is one of the relatively few such dissertations that have become a by-word. In it the methods, novel for that time, of Fourier analysis on groups of "adeles", were worked out to recover Hecke's results.

Subsequently Tate worked with Emil Artin to give a treatment of class field theory based on cohomology of groups, explaining the content as the Galois cohomology of idele classes, and introduced Tate cohomology groups. In the following decades Tate extended the reach of Galois cohomology: Poitou-Tate duality, abelian varieties, the Tate-Shafarevich group, and relations with algebraic K-theory.

He made a number of individual and important contributions to p-adic theory: the Lubin-Tate local theory of complex multiplication of formal groups; rigid analytic spaces; the 'Tate curve' parametrisation for certain p-adic elliptic curves; p-divisible (Tate-Barsotti) groups. Many of his results were not immediately published and were written up by Jean-Pierre Serre. They collaborated on a major published paper on good reduction of abelian varieties.

The Tate conjectures are the equivalent for étale cohomology of the Hodge conjecture. They relate to the Galois action on the l-adic cohomology of an algebraic variety, identifying a space of 'Tate cycles' (the fixed cycles for a suitably Tate-twisted action) that conjecturally picks out the algebraic cycles. A special case of the conjectures, which are open in the general case, was involved in the proof of the Mordell conjecture by Gerd Faltings.

Tate has had a profound influence on the development of number theory through his role as aPhD advisor. His students include Joe Buhler, Benedict Gross, Robert Kottwitz, James Milne, Carl Pomerance, Ken Ribet and Joseph H. Silverman.

He was awarded a Wolf Prize in Mathematics in 2002/3.

ee also

*Sato-Tate conjecture
*Sato-Tate measure
*Tate module
*Néron–Tate height

elected publications

*J. Tate, "Fourier analysis in number fields and Hecke's zeta functions" (Tate's 1950 thesis), reprinted in "Algebraic Number Theory" by J. W. S. Cassels, A. Frohlich ISBN 0-12-163251-2

External links

* [http://www.ma.utexas.edu/text/webpages/tate.html Tate's home page]
*MathGenealogy|id=7652


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  • John Tate — John Torrence Tate Jr. (*13 de marzo de 1925, Minneapolis, Minnesota ) es un matemático estadounidense, distinguido por sus muchas contribuciones fundamentales a la Teoría de números algebraicos y áreas afines en geometría algebraica. Él obtuvo… …   Wikipedia Español

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  • John Tate (mathématicien) — Pour les articles homonymes, voir John Tate (boxeur) et Tate. John Torrence Tate Jr. (13 mars 1925 à Minneapolis) est un mathématicien américain. En 2010, il a reçu le prix Abel pour ses travaux en théorie des nombres. John Tate est… …   Wikipédia en Français

  • John T. Tate — John Torrence Tate (* 13. März 1925 in Minneapolis, Minnesota) ist ein US amerikanischer Mathematiker, der auf den Feldern Algebraische Geometrie und Zahlentheorie arbeitet. Leben und Werk Nach drei Jahren in der US Navy erhielt er seinen B.A.… …   Deutsch Wikipedia

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  • John Torrence Tate (físico) — John Torrence Tate (Adams County, Iowa, 28 de julio, 1889 27 de mayo, 1950) fue un físico estadounidense que trabajó principalmente como profesor e investigador en la universidad de Minnesota, en las áreas de la mecánica cuántica y la física… …   Wikipedia Español

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