Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

   
 
 

 

Recent progress on the Tate conjecture


Author: Burt Totaro
Journal: Bull. Amer. Math. Soc. 54 (2017), 575-590
MSC (2010): Primary 14C25; Secondary 14F20, 14G15, 14J28
DOI: https://doi.org/10.1090/bull/1588
Published electronically: June 16, 2017
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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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Additional Information

Burt Totaro
Affiliation: UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555
Email: totaro@math.ucla.edu

DOI: https://doi.org/10.1090/bull/1588
Received by editor(s): May 30, 2017
Published electronically: June 16, 2017
Additional Notes: This work was supported by NSF grant DMS-1303105.
Article copyright: © Copyright 2017 by the author