Mod $p$ sheaves on Witt flags
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912257115422720 |
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| author | Cass, Robert Lourenço, João |
| author_facet | Cass, Robert Lourenço, João |
| contents | We characterize Cohen--Macaulay and $φ$-rational perfect schemes in terms of their perverse étale mod $p$ sheaves. Using inversion of adjunction, we prove that sufficiently small Schubert varieties in the Witt affine flag variety are perfections of globally $+$-regular varieties, and hence they are $φ$-rational. Our methods apply uniformly to all affine Schubert varieties in equicharacteristic, as well as classical Schubert varieties, thereby answering a question of Bhatt. As a corollary, we deduce that scheme-theoretic local models always have $φ$-split special fiber. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mod $p$ sheaves on Witt flags Cass, Robert Lourenço, João Algebraic Geometry Commutative Algebra Number Theory Representation Theory 14M15 (Primary), 13A35, 13D45, 14G17 (Secondary) We characterize Cohen--Macaulay and $φ$-rational perfect schemes in terms of their perverse étale mod $p$ sheaves. Using inversion of adjunction, we prove that sufficiently small Schubert varieties in the Witt affine flag variety are perfections of globally $+$-regular varieties, and hence they are $φ$-rational. Our methods apply uniformly to all affine Schubert varieties in equicharacteristic, as well as classical Schubert varieties, thereby answering a question of Bhatt. As a corollary, we deduce that scheme-theoretic local models always have $φ$-split special fiber. |
| title | Mod $p$ sheaves on Witt flags |
| topic | Algebraic Geometry Commutative Algebra Number Theory Representation Theory 14M15 (Primary), 13A35, 13D45, 14G17 (Secondary) |
| url | https://arxiv.org/abs/2503.01796 |