UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

被引：5

作者：

Shankar, Ananth N. ^{[1
]}

Tsimerman, Jacob ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Toronto, Dept Math, Toronto, ON, Canada

来源：

FORUM OF MATHEMATICS SIGMA | 2018年 / 6卷

关键词：

ORDINARY ABELIAN-VARIETIES; MODULI SPACES; FOLIATIONS;

D O I：

10.1017/fms.2018.15

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a heuristic argument based on Honda-Tate theory against many conjectures in 'unlikely intersections' over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian. Using methods of additive combinatorics, we answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve.

引用

页数：17

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