Tate helped shape the great reformulation of arithmetic and geometry which has taken
place since the 1950s
Andrew Wiles (Introduction to Tate's talk at the conference on
the Millenium Prizes, 2000).
This is my article on Tate's work for the second volume in the book
series on the Abel Prize winners. True to the epigraph, I have attempted to
explain it in the context of the "great reformulation".
- Hecke L-series and the cohomology of number fields
- Abelian varieties and curves
- Rigid analytic spaces
- The Tate conjecture
- Lubin-Tate theory and Barsotti-Tate group schemes
- Elliptic curves
- The K-theory of number fields
- The Stark conjectures
- Noncommutative ring theory
- Miscellaneous articles
First posted 18.03.12, 72 pages.
23.09.12. (Many minor fixes; thanks to Timo Keller and Matthias Künzer.)
03.12.12. (Minor fixes).
One correction: "Nakayama (1957)" is a reference to T. Nakayama, Cohomology of class field theory and tensor product modules I, Ann. of
Math., 65 (1957), pp. 255-267.