Theta Operator Equals Fontaine Operator on Modular Curves
| Autor: | Jiang, Yuanyang |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\rho_{f}$ is irreducible, then $f$ is classical if and only if $\rho_{f}$ is de Rham at $p$. For the proof, we prove that theta operator $\theta^{k}$ coincides with Fontaine operator in a suitable sense. Comment: 53 pages. Comments welcome! |
| Databáze: | arXiv |
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