Unlikely Intersections in Finite Characteristic

Ananth N Shankar; Jacob Tsimerman

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arXiv · 1610.03552

Unlikely Intersections in Finite Characteristic

Ananth N Shankar·Jacob Tsimerman

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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.

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Ananth N Shankar, Jacob Tsimerman. 2016-10-11. Unlikely Intersections in Finite Characteristic. https://arxiv.org/abs/1610.03552

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