Local systems which do not come from abelian varieties
Algebraic Geometry
2025-02-13 v2 Number Theory
Abstract
For each smooth curve over a finite field, after puncturing it at finitely many points, we construct local systems on it of geometric origin which do not come from a family of abelian varieties. We do so by proving a criterion which must be satisfied by local systems which do come from abelian varieties, inspired by an analogous Hodge theoretic criterion in characteristic zero.
Cite
@article{arxiv.2408.02475,
title = {Local systems which do not come from abelian varieties},
author = {Paul Brommer-Wierig and Yeuk Hay Joshua Lam},
journal= {arXiv preprint arXiv:2408.02475},
year = {2025}
}