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.
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页数：17
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