UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC

Author(s)
Shankar, Ananth; Tsimerman, Jacob
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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 answer a related question of Chai and Oort where the ambient Shimura variety is a power of the modular curve.
Date issued
2018-08
URI
https://hdl.handle.net/1721.1/122793
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Forum of Mathematics, Sigma
Publisher
Cambridge University Press (CUP)
Citation
Shankar, A. and Tsimerman, J. UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC. Forum of Mathematics, Sigma, 6 (August 2018): E13 © 2018 The Author(s)
Version: Final published version
ISSN
2050-5094
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