A note on some $p$-adic analytic Hecke actions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866914430153916416 |
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| author | Pan, Lue |
| author_facet | Pan, Lue |
| contents | We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge-Tate-Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_11845 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A note on some $p$-adic analytic Hecke actions Pan, Lue Number Theory 11F33 We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge-Tate-Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa. |
| title | A note on some $p$-adic analytic Hecke actions |
| topic | Number Theory 11F33 |
| url | https://arxiv.org/abs/2012.11845 |