The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916594818482176 |
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| author | Betina, Adel Maksoud, Alexandre Pozzi, Alice |
| author_facet | Betina, Adel Maksoud, Alexandre Pozzi, Alice |
| contents | A complete description of the local geometry of the $p$-adic eigencurve at $p$-irregular classical weight one cusp forms is given in the cases where the usual $R=T$ methods fall short. As an application, we show that the ordinary $p$-adic étale cohomology group attached to the tower of elliptic modular curves $X_1(Np^r)$ is not free over the Hecke algebra, when localized at a $p$-irregular weight one point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators Betina, Adel Maksoud, Alexandre Pozzi, Alice Number Theory 11F33, 11G18 (Primary) 11F80, 11R23 (Secondary) A complete description of the local geometry of the $p$-adic eigencurve at $p$-irregular classical weight one cusp forms is given in the cases where the usual $R=T$ methods fall short. As an application, we show that the ordinary $p$-adic étale cohomology group attached to the tower of elliptic modular curves $X_1(Np^r)$ is not free over the Hecke algebra, when localized at a $p$-irregular weight one point. |
| title | The eigencurve at crystalline points with scalar Frobenius and Gross-Stark regulators |
| topic | Number Theory 11F33, 11G18 (Primary) 11F80, 11R23 (Secondary) |
| url | https://arxiv.org/abs/2502.00876 |