TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Yuri G. Zarhin

doi:10.5802/aif.3483

TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Yuri G. Zarhin

Mathematics

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1 Scopus citations

Abstract

We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X^2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

Original language	English (US)
Pages (from-to)	2339-2383
Number of pages	45
Journal	Annales de l'Institut Fourier
Volume	72
Issue number	6
DOIs	https://doi.org/10.5802/aif.3483
State	Published - 2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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10.5802/aif.3483

Cite this

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title = "TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS",

abstract = "We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.",

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AB - We deal with g-dimensional abelian varieties X over finite fields. We prove that there is a universal constant (positive integer) N = N(g) that depends only on g that enjoys the following property. If a certain self-product of X carries an exotic Tate class then the self-product X2N of X also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

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ER -

TATE CLASSES ON SELF-PRODUCTS OF ABELIAN VARIETIES OVER FINITE FIELDS

Abstract

All Science Journal Classification (ASJC) codes

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