Lattices in Tate modules

被引：2
|
作者：
Poonen, Bjorn [1 ]
Rybakov, Sergey [2 ,3 ]
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Russian Acad Sci, Inst Informat Transmiss Problems, Lab 13, Moscow 127051, Russia
[3] Interdisciplinary Sci Ctr JV Poncelet, Moscow 119002, Russia
来源：
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2021年 / 118卷 / 49期
关键词：
abelian variety; Tate module; endomorphism; Dieudonne module; ABELIAN-VARIETIES;
D O I：
10.1073/pnas.2113201118
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Refining a theorem of Zarhin, we prove that, given a g dimensional abelian variety X and an endomorphism u of X, there exists a matrix A is an element of M-2g(Z) such that each Tate module TeX has a Ze-basis on which the action of u is given by A, and similarly for the covariant Dieudonne module if over a perfect field of characteristic p.
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页数：3
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