Compatibility of canonical $\ell$-adic local systems on Shimura varieties, II

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Main Author: Patrikis, Stefan
Format: Preprint
Published: 2025
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author Patrikis, Stefan
author_facet Patrikis, Stefan
contents Let $(G, X)$ be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical $G(\mathbb{Q}_{\ell})$-valued local systems on Shimura varieties for $G$ form compatible systems after projection to the adjoint group of $G$. In this note, we strengthen this result to prove compatibility for the $G(\mathbb{Q}_{\ell})$-local systems themselves. We also include the crystalline compatibility, extending the adjoint case established in our joint work Jake Huryn, Kiran Kedlaya, and Christian Klevdal.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00305
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Compatibility of canonical $\ell$-adic local systems on Shimura varieties, II
Patrikis, Stefan
Number Theory
Algebraic Geometry
11G18, 14G35
Let $(G, X)$ be a Shimura datum. In previous work with Christian Klevdal, we showed that the canonical $G(\mathbb{Q}_{\ell})$-valued local systems on Shimura varieties for $G$ form compatible systems after projection to the adjoint group of $G$. In this note, we strengthen this result to prove compatibility for the $G(\mathbb{Q}_{\ell})$-local systems themselves. We also include the crystalline compatibility, extending the adjoint case established in our joint work Jake Huryn, Kiran Kedlaya, and Christian Klevdal.
title Compatibility of canonical $\ell$-adic local systems on Shimura varieties, II
topic Number Theory
Algebraic Geometry
11G18, 14G35
url https://arxiv.org/abs/2504.00305