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Recent progress on the Tate conjecture

Published Web Location

https://doi.org/10.1090/bull/1588
Creative Commons 'BY-ND' version 4.0 license
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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