Localized Gouvêa-Mazur conjecture
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914734638366720 |
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| author | Ren, Rufei |
| author_facet | Ren, Rufei |
| contents | Gouvêa-Mazur [GM] made a conjecture on the local constancy of slopes of modular forms when the weight varies $p$-adically. Since one may decompose the space of modular forms according to associated residual Galois representations, the Gouvêa-Mazur conjecture makes sense for each such component. We prove the localized Gouvêa-Mazur conjecture when the residual Galois representation is irreducible and its restriction to $\textrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ is reducible and very generic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11577 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Localized Gouvêa-Mazur conjecture Ren, Rufei Number Theory 11F33, 11F85 Gouvêa-Mazur [GM] made a conjecture on the local constancy of slopes of modular forms when the weight varies $p$-adically. Since one may decompose the space of modular forms according to associated residual Galois representations, the Gouvêa-Mazur conjecture makes sense for each such component. We prove the localized Gouvêa-Mazur conjecture when the residual Galois representation is irreducible and its restriction to $\textrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ is reducible and very generic. |
| title | Localized Gouvêa-Mazur conjecture |
| topic | Number Theory 11F33, 11F85 |
| url | https://arxiv.org/abs/2206.11577 |