On the pro-modularity in the residually reducible case for some totally real fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915404898631680 |
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| author | Zhang, Xinyao |
| author_facet | Zhang, Xinyao |
| contents | In this article, we study the relation between the universal deformation rings and big Hecke algebras in the residually reducible case. Following the strategy of Skinner-Wiles and Pan's proof of the Fontaine-Mazur conjecture, we prove a pro-modularity result. Based on this result, we also give a conditional big $R=\mathbb{T}$ theorem over some totally real fields, which is a generalization of Deo's result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the pro-modularity in the residually reducible case for some totally real fields Zhang, Xinyao Number Theory In this article, we study the relation between the universal deformation rings and big Hecke algebras in the residually reducible case. Following the strategy of Skinner-Wiles and Pan's proof of the Fontaine-Mazur conjecture, we prove a pro-modularity result. Based on this result, we also give a conditional big $R=\mathbb{T}$ theorem over some totally real fields, which is a generalization of Deo's result. |
| title | On the pro-modularity in the residually reducible case for some totally real fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.18661 |