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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.06812 |
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| _version_ | 1866908460955729920 |
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| author | Zhang, Xinyao |
| author_facet | Zhang, Xinyao |
| contents | In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over $\Gal(\overline{\Q}/\Q)$ when $p=3$, hence concluding the conjecture in the regular case for all odd primes. Our result is a sequel to Pan's work, based on some recent progress on $p$-adic Langlands correspondence, Galois deformation theory and a potential pro-modularity result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Fontaine-Mazur conjecture for $p=3$ Zhang, Xinyao Number Theory In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over $\Gal(\overline{\Q}/\Q)$ when $p=3$, hence concluding the conjecture in the regular case for all odd primes. Our result is a sequel to Pan's work, based on some recent progress on $p$-adic Langlands correspondence, Galois deformation theory and a potential pro-modularity result. |
| title | On the Fontaine-Mazur conjecture for $p=3$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.06812 |