
John Tate Biography 
John Torrence Tate, 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 19541990, and is now at the University of Texas at Austin.
Tate's thesis, on the analytic properties of the class of Lfunction introduced by Erich Hecke, is one of the relatively few such dissertations that have become a byword. 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. In the following decades Tate extended the reach of Galois cohomology: duality, abelian varieties, the TateShafarevich group, and relations with algebraic Ktheory.
He made a number of individual and important contributions to padic theory: the LubinTate local theory of complex multiplication of formal groups; rigid analytic spaces; the 'Tate curve' parametrisation for padic elliptic curves; pdivisible (TateBarsotti) groups. Many of his results were not immediately published and were written up by JeanPierre Serre. They collaborated on a major published paper on abelian varieties.
The Tate conjectures are the equivalent for etale cohomology of the Hodge conjecture. They relate to the Galois action on the ladic cohomology of an algebraic variety, identifying a space of 'Tate cycles' (the fixed cycles for a suitably Tatetwisted 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. 

John Tate Resources 



