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A note on Tate's conjectures for abelian varieties

Chao Li and Wei Zhang

Vol. 1 (2022), No. 1, 41–50
Abstract

In this mostly expository note, we explain a proof of Tate’s two conjectures for algebraic cycles of arbitrary codimension on certain products of elliptic curves and abelian surfaces over number fields.

Keywords
Tate conjecture, abelian varieties, algebraic cycles, poles of zeta functions, potential automorphy
Mathematical Subject Classification
Primary: 11G40, 14G10
Secondary: 11G10, 14C25
Milestones
Received: 9 January 2022
Revised: 9 May 2022
Accepted: 19 May 2022
Published: 26 October 2022
Authors
Chao Li
Department of Mathematics
Columbia University
New York, NY
United States
Wei Zhang
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States