Auslander regularity of $p$-adic Banach algebras via almost mathematics
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910810594344960 |
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| author | Bode, Andreas |
| author_facet | Bode, Andreas |
| contents | We discuss an "almost" version of Auslander regularity and use it to prove the Auslander regularity of various Banach algebras over non-discretely valued fields appearing naturally in $p$-adic locally analytic representation theory: completed Weyl algebras, the completed enveloping algebra of a Lie algebra, and the Banach completion of the distribution algebra $D(G, K)$ for a compact $p$-adic Lie group $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Auslander regularity of $p$-adic Banach algebras via almost mathematics Bode, Andreas Representation Theory Number Theory Rings and Algebras 16E65 (primary), 14G22 (secondary) We discuss an "almost" version of Auslander regularity and use it to prove the Auslander regularity of various Banach algebras over non-discretely valued fields appearing naturally in $p$-adic locally analytic representation theory: completed Weyl algebras, the completed enveloping algebra of a Lie algebra, and the Banach completion of the distribution algebra $D(G, K)$ for a compact $p$-adic Lie group $G$. |
| title | Auslander regularity of $p$-adic Banach algebras via almost mathematics |
| topic | Representation Theory Number Theory Rings and Algebras 16E65 (primary), 14G22 (secondary) |
| url | https://arxiv.org/abs/2502.01119 |