Auslander regularity of completed rings of $p$-adic differential operators
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914189798277120 |
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| author | Bode, Andreas |
| author_facet | Bode, Andreas |
| contents | We prove that any smooth rigid analytic variety $X$ admits an affinoid covering $\{U_i\}$ such that the Banach algebras involved in the Fréchet--Stein presentation of the completed ring of differential operators D-cap$(U_i)$ are Auslander regular for each $i$. We use this result to prove projection formulae and adjunction results for coadmissible D-cap-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Auslander regularity of completed rings of $p$-adic differential operators Bode, Andreas Number Theory Rings and Algebras Representation Theory 14G22, 14F10 We prove that any smooth rigid analytic variety $X$ admits an affinoid covering $\{U_i\}$ such that the Banach algebras involved in the Fréchet--Stein presentation of the completed ring of differential operators D-cap$(U_i)$ are Auslander regular for each $i$. We use this result to prove projection formulae and adjunction results for coadmissible D-cap-modules. |
| title | Auslander regularity of completed rings of $p$-adic differential operators |
| topic | Number Theory Rings and Algebras Representation Theory 14G22, 14F10 |
| url | https://arxiv.org/abs/2505.08001 |