De Rham $F$-gauges and Shimura varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908536116609024 |
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| author | Shen, Xu |
| author_facet | Shen, Xu |
| contents | We study $F$-gauges for de Rham cohomology of smooth algebraic varieties in characteristic $p$. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl-Oort stratifications by constructing universal de Rham $F$-gauges with $G$-structure. We also study the cohomology of de Rham $F$-gauges on these varieties. In particular, in the PEL type case and when the weights of the flat automorphic vector bundles are $p$-small, we determine the $F$-gauge structure on their de Rham cohomology by the associated dual BGG complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | De Rham $F$-gauges and Shimura varieties Shen, Xu Algebraic Geometry Number Theory 11G18, 14G35 We study $F$-gauges for de Rham cohomology of smooth algebraic varieties in characteristic $p$. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl-Oort stratifications by constructing universal de Rham $F$-gauges with $G$-structure. We also study the cohomology of de Rham $F$-gauges on these varieties. In particular, in the PEL type case and when the weights of the flat automorphic vector bundles are $p$-small, we determine the $F$-gauge structure on their de Rham cohomology by the associated dual BGG complexes. |
| title | De Rham $F$-gauges and Shimura varieties |
| topic | Algebraic Geometry Number Theory 11G18, 14G35 |
| url | https://arxiv.org/abs/2403.01899 |