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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.14243 |
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| _version_ | 1866908874520395776 |
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| author | Jiang, Yuanyang |
| author_facet | Jiang, Yuanyang |
| contents | Inspired by [Pan22], we give a new proof that for an overconvergent modular eigenform $f$ of weight $1+k$ with $k\in\mathbb{Z}_{\ge1}$, assuming that its associated global Galois representation $ρ_{f}$ is irreducible, then $f$ is classical if and only if $ρ_{f}$ is de Rham at $p$. For the proof, we prove that theta operator $θ^{k}$ coincides with Fontaine operator in a suitable sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14243 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theta Operator Equals Fontaine Operator on Modular Curves Jiang, Yuanyang Number Theory 14G35, 11F17, 11F18 Inspired by [Pan22], we give a new proof that for an overconvergent modular eigenform $f$ of weight $1+k$ with $k\in\mathbb{Z}_{\ge1}$, assuming that its associated global Galois representation $ρ_{f}$ is irreducible, then $f$ is classical if and only if $ρ_{f}$ is de Rham at $p$. For the proof, we prove that theta operator $θ^{k}$ coincides with Fontaine operator in a suitable sense. |
| title | Theta Operator Equals Fontaine Operator on Modular Curves |
| topic | Number Theory 14G35, 11F17, 11F18 |
| url | https://arxiv.org/abs/2310.14243 |