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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2306.09696 |
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| _version_ | 1866911323400437760 |
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| author | Timmins, James |
| author_facet | Timmins, James |
| contents | Let F be a non-trivial finite extension of the p-adic numbers, and G be a compact p-adic Lie group whose Lie algebra is isomorphic to a split semisimple F-Lie algebra. We prove that the mod p Iwasawa algebra of G has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod p smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of $GL_n(F)$, with central character, has finite length if its dual has canonical dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09696 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The canonical dimension of modules for Iwasawa algebras Timmins, James Number Theory Rings and Algebras Representation Theory 16P60, 16P90, 22E50 Let F be a non-trivial finite extension of the p-adic numbers, and G be a compact p-adic Lie group whose Lie algebra is isomorphic to a split semisimple F-Lie algebra. We prove that the mod p Iwasawa algebra of G has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod p smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of $GL_n(F)$, with central character, has finite length if its dual has canonical dimension two. |
| title | The canonical dimension of modules for Iwasawa algebras |
| topic | Number Theory Rings and Algebras Representation Theory 16P60, 16P90, 22E50 |
| url | https://arxiv.org/abs/2306.09696 |