Tate classes on self-products of Abelian varieties over finite fields

IF 0.8 4区数学 Q2 MATHEMATICS

Annales De L Institut Fourier Pub Date : 2020-05-09 DOI:10.5802/aif.3483

Y. Zarhin

引用次数: 1

Abstract

We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. 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.

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有限域上阿贝尔变的自积上的泰特类

我们处理有限域上的$g$维阿贝尔变量$X$。我们证明了存在一个仅依赖于$g$的普适常数(正整数)$ N=N(g)$，它具有下列性质。如果$X$的某个自积$X$携带一个奇异的Tate类，那么$X$的自积$X^{2N}$也携带一个奇异的Tate类。这对Kiran Kedlaya的问题给出了肯定的回答。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Fourier 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

1 months

期刊介绍： The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French. The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.