Recent progress on the Tate conjecture-Reference-Cited by-同舟云学术

Recent progress on the Tate conjecture

Published:2017-06-16 Issue:4 Volume:54 Page:575-590
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

Totaro Burt

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/2017-54-04/S0273-0979-2017-01588-1/S0273-0979-2017-01588-1.pdf

Reference48 articles.

1. On the Shafarevich and Tate conjectures for hyper-Kähler varieties;André, Yves;Math. Ann.,1996

2. Panoramas et Synth\`eses [Panoramas and Syntheses];André, Yves,2004

3. The Shafarevich-Tate conjecture for pencils of elliptic curves on 𝐾3 surfaces;Artin, M.;Invent. Math.,1973

4. Construction de courbes sur les surfaces K3 (d’après Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik…);Benoist, Olivier;Ast\'{e}risque,2015

5. Notes on elliptic curves. II;Birch, B. J.;J. Reine Angew. Math.,1965

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