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arXiv · 2408.02475

Local systems which do not come from abelian varieties

Paul Brommer-Wierig·Yeuk Hay Joshua Lam
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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.

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Paul Brommer-Wierig, Yeuk Hay Joshua Lam. 2024-08-05. Local systems which do not come from abelian varieties. https://arxiv.org/abs/2408.02475

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