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UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

Published online by Cambridge University Press:  09 August 2018

ANANTH N. SHANKAR  and
JACOB TSIMERMAN
ANANTH N. SHANKAR
Affiliation:
Department of Mathematics, MIT, Cambridge, MA, USA; ananth.shnkr@gmail.com
JACOB TSIMERMAN
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, Canada; jacobt@math.toronto.edu

Abstract

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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.

Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e13
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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