Systems of Hecke eigenvalues on subschemes of Shimura varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912033560068096 |
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| author | Reppen, Stefan |
| author_facet | Reppen, Stefan |
| contents | We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod $p$ abelian type compact Shimura variety at hyperspecial level are the same as those appearing in any Hecke-equivariant closed subscheme. We also prove analogous results for noncompact Shimura varieties or nonclosed subschemes, such as Ekedahl-Oort strata, length strata and central leaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Systems of Hecke eigenvalues on subschemes of Shimura varieties Reppen, Stefan Number Theory Algebraic Geometry We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod $p$ abelian type compact Shimura variety at hyperspecial level are the same as those appearing in any Hecke-equivariant closed subscheme. We also prove analogous results for noncompact Shimura varieties or nonclosed subschemes, such as Ekedahl-Oort strata, length strata and central leaves. |
| title | Systems of Hecke eigenvalues on subschemes of Shimura varieties |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2409.11720 |