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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



A remark on the Tate Conjecture

Author: Ben Moonen
Journal: J. Algebraic Geom. 28 (2019), 599-603
Published electronically: April 24, 2019
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Abstract | References | Additional Information

Abstract: The strong version of the Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations and an assertion (T) which says that every Tate class is algebraic. We show that in characteristic $0$, (T) implies (S). In characteristic $p$ an analogous result is true under stronger assumptions.

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Additional Information

Ben Moonen
Affiliation: IMAPP, Radboud University, P.O. Box 9010, 6500GL Nijmegen, The Netherlands
MR Author ID: 254842

Received by editor(s): September 29, 2017
Received by editor(s) in revised form: January 25, 2018
Published electronically: April 24, 2019
Article copyright: © Copyright 2019 University Press, Inc.