标题： 有限特征中的不相交性 显示英文标题

标题： Unlikely Intersections in Finite Characteristic

摘要： 我们提出一个基于本田-塔特定理的启发式论点，反对有限域代数闭包上的“不寻常交集”中的许多猜想；特别是，我们猜想每个4维的阿贝尔簇都与一个雅可比簇同源。 使用加性组合学的方法，我们能够对柴和奥特的一个相关问题给出否定回答，其中环境辛托里变体是模曲线的幂。 显示英文摘要

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 are able to give a negative answer to a related question of Chai and Oort where the ambient Shimura Variety is a power of the modular curve.