We deal with -dimensional abelian varieties over finite fields. We prove that there is a universal constant (positive integer) that depends only on that enjoys the following property. If a certain self-product of carries an exotic Tate class then the self-product of also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.
Nous étudions des variétés abéliennes de dimension sur des corps finis. Nous prouvons l’existence d’une constante universelle (entière positive) , qui ne dépend que de et a la propriété suivante : si une certaine puissance de admet une classe de Tate exotique, la puissance de admet une classe de Tate exotique aussi. Cela donne une réponse positive à une question de Kiran Kedlaya.
Revised:
Accepted:
Published online:
Keywords: Abelian varieties, Tate classes, Finite fields
Mot clés : Variétés abéliennes, classes de Tate, corps finis
Zarhin, Yuri G. 1
@article{AIF_2022__72_6_2339_0, author = {Zarhin, Yuri G.}, title = {Tate classes on self-products of {Abelian} varieties over finite fields}, journal = {Annales de l'Institut Fourier}, pages = {2339--2383}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {6}, year = {2022}, doi = {10.5802/aif.3483}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3483/} }
TY - JOUR AU - Zarhin, Yuri G. TI - Tate classes on self-products of Abelian varieties over finite fields JO - Annales de l'Institut Fourier PY - 2022 SP - 2339 EP - 2383 VL - 72 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3483/ DO - 10.5802/aif.3483 LA - en ID - AIF_2022__72_6_2339_0 ER -
%0 Journal Article %A Zarhin, Yuri G. %T Tate classes on self-products of Abelian varieties over finite fields %J Annales de l'Institut Fourier %D 2022 %P 2339-2383 %V 72 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3483/ %R 10.5802/aif.3483 %G en %F AIF_2022__72_6_2339_0
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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