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).

Abstract

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".

Contents

1. Hecke L-series and the cohomology of number fields
2. Abelian varieties and curves
3. Rigid analytic spaces
4. The Tate conjecture
5. Lubin-Tate theory and Barsotti-Tate group schemes
6. Elliptic curves
7. The K-theory of number fields
8. The Stark conjectures
9. Noncommutative ring theory
10. Miscellaneous articles

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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).