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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21637 |
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| _version_ | 1866913914741063680 |
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| author | Wiersema, Hanneke |
| author_facet | Wiersema, Hanneke |
| contents | Let $p$ be an odd prime. Let $K/\mathbb{Q}_p$ be a finite unramified extension. Let $ρ: G_K \to GL_2(\overline{\mathbb{F}}_p)$ be a continuous representation. We prove that $ρ$ has a crystalline lift of small irregular weight if and only if it has multiple crystalline lifts of certain specified regular weights. The inspiration for this result comes from work of Diamond-Sasaki on geometric Serre weight conjectures. Our result provides a way to translate results currently formulated only for regular weights to also include irregular weights. The proof uses results on Kisin and $(φ,\hat{G})$-modules obtained from extending recent work of Gee-Liu-Savitt to study crystalline liftability of irregular weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crystalline liftability of irregular weights Wiersema, Hanneke Number Theory 11F80 Let $p$ be an odd prime. Let $K/\mathbb{Q}_p$ be a finite unramified extension. Let $ρ: G_K \to GL_2(\overline{\mathbb{F}}_p)$ be a continuous representation. We prove that $ρ$ has a crystalline lift of small irregular weight if and only if it has multiple crystalline lifts of certain specified regular weights. The inspiration for this result comes from work of Diamond-Sasaki on geometric Serre weight conjectures. Our result provides a way to translate results currently formulated only for regular weights to also include irregular weights. The proof uses results on Kisin and $(φ,\hat{G})$-modules obtained from extending recent work of Gee-Liu-Savitt to study crystalline liftability of irregular weights. |
| title | Crystalline liftability of irregular weights |
| topic | Number Theory 11F80 |
| url | https://arxiv.org/abs/2506.21637 |