Unlikely Intersections in Finite Characteristic
Number Theory
2016-10-19 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1610.03552,
title = {Unlikely Intersections in Finite Characteristic},
author = {Ananth N Shankar and Jacob Tsimerman},
journal= {arXiv preprint arXiv:1610.03552},
year = {2016}
}
Comments
Corrected mistakes, added references, and reduced exponent of modular curve from 462 to 270