Compatibility of canonical $\ell$-adic local systems on Shimura varieties, II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909595436318720 |
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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 |