Angle ranks of abelian varieties

被引：1

作者：

Dupuy, Taylor ^{[2
]}

Kedlaya, Kiran S. ^{[1
]}

Zureick-Brown, David ^{[3
]}

机构：

[1] Univ Calif San Diego, Dept Math, 9500 Gilman Dr,0112, La Jolla, CA 92093 USA

[2] Univ Vermont, Burlington, VT USA

[3] Amherst Coll, Amherst, MA USA

来源：

MATHEMATISCHE ANNALEN | 2024年 / 389卷 / 01期

基金：

美国国家科学基金会;

关键词：

REPRESENTATIONS; CONJECTURE; FINITE; CYCLES;

D O I：

10.1007/s00208-023-02633-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the formalism of Newton hyperplane arrangements, we resolve the open questions regarding angle rank left over from work of the first two authors with Roe and Vincent. As a consequence we end up generalizing theorems of Lenstra-Zarhin and Tankeev proving several new cases of the Tate conjecture for abelian varieties over finite fields. We also obtain an effective version of a recent theorem of Zarhin bounding the heights of coefficients in multiplicative relations among Frobenius eigenvalues.

引用

页码：169 / 185

页数：17

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