Recent progress on the Tate conjecture

Totaro, Burt

doi:10.1090/bull/1588

Recent progress on the Tate conjecture
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Bull. Amer. Math. Soc. 54 (2017), 575-590

Abstract:

We survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely related with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. We conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.

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