Tate classes on self-products of Abelian varieties over finite fields
Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2339-2383.

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.

Nous étudions des variétés abéliennes X de dimension g sur des corps finis. Nous prouvons l’existence d’une constante universelle (entière positive) N=N(g), qui ne dépend que de g et a la propriété suivante : si une certaine puissance de X admet une classe de Tate exotique, la puissance X 2N de X admet une classe de Tate exotique aussi. Cela donne une réponse positive à une question de Kiran Kedlaya.

Received:
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Accepted:
Published online:
DOI: 10.5802/aif.3483
Classification: 11G10,  11G25,  14G15
Keywords: Abelian varieties, Tate classes, Finite fields
Zarhin, Yuri G. 1

1 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Zarhin, Yuri G. Tate classes on self-products of Abelian varieties over finite fields. Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2339-2383. doi : 10.5802/aif.3483. https://aif.centre-mersenne.org/articles/10.5802/aif.3483/

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