Compactifications of Iwahori-level Hilbert modular varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909574294929408 |
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| author | Diamond, Fred |
| author_facet | Diamond, Fred |
| contents | We study minimal and toroidal compactifications of $p$-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over $p$, and extend it to certain finer level structures. We also prove extensions to compactifications of recent results on Iwahori-level Kodaira--Spencer isomorphisms and cohomological vanishing for degeneracy maps. Finally we apply the theory to study $q$-expansions of Hilbert modular forms, especially the effect of Hecke operators at primes over $p$ over general base rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06922 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Compactifications of Iwahori-level Hilbert modular varieties Diamond, Fred Number Theory 11F41 (Primary), 11G18, 11F30 (Secondary) We study minimal and toroidal compactifications of $p$-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over $p$, and extend it to certain finer level structures. We also prove extensions to compactifications of recent results on Iwahori-level Kodaira--Spencer isomorphisms and cohomological vanishing for degeneracy maps. Finally we apply the theory to study $q$-expansions of Hilbert modular forms, especially the effect of Hecke operators at primes over $p$ over general base rings. |
| title | Compactifications of Iwahori-level Hilbert modular varieties |
| topic | Number Theory 11F41 (Primary), 11G18, 11F30 (Secondary) |
| url | https://arxiv.org/abs/2211.06922 |