Lifts of Supersingular Abelian Varieties With Small Mumford-Tate Groups

被引：0

作者：

Lam, Yeuk Hay Joshua ^{[1
]}

Oswal, Abhishek ^{[2
]}

机构：

[1] IHES, 35 Rte Chartres, F-91440 Bures Sur Yvette, France

[2] Caltech, Div Phys Math & Astron, Pasadena, CA 91125 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 10期

关键词：

D O I：

10.1093/imrn/rnad261

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate to what extent an abelian variety over a finite field can be lifted to one in characteristic zero with small Mumford-Tate group. We prove that supersingular abelian surfaces, respectively three-folds, can be lifted to ones isogenous to a square, respectively product, of elliptic curves. On the other hand, we show that supersingular abelian three-folds cannot be lifted to one isogenous to the cube of an elliptic curve over the Witt vectors.

引用

页码：8384 / 8401

页数：18

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