Ramification bounds via Wach modules and q-crystalline cohomology
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911722023944192 |
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| author | Čoupek, Pavel |
| author_facet | Čoupek, Pavel |
| contents | Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance of $q$-crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of $\mathrm{H}^{i}_{et}(X_{\mathbb{C}_K}, \mathbb{Z}/p\mathbb{Z})$ for a smooth proper $p$-adic formal scheme $X$ over $\mathcal{O}_K$, for arbitrarily large degree $i$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ramification bounds via Wach modules and q-crystalline cohomology Čoupek, Pavel Number Theory Algebraic Geometry 11F80, 14F30, 11F85, 14G20, 11S15 Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an instance of $q$-crystalline cohomology (in its prismatic form), we thus obtain improved bounds on the ramification of $\mathrm{H}^{i}_{et}(X_{\mathbb{C}_K}, \mathbb{Z}/p\mathbb{Z})$ for a smooth proper $p$-adic formal scheme $X$ over $\mathcal{O}_K$, for arbitrarily large degree $i$. |
| title | Ramification bounds via Wach modules and q-crystalline cohomology |
| topic | Number Theory Algebraic Geometry 11F80, 14F30, 11F85, 14G20, 11S15 |
| url | https://arxiv.org/abs/2410.23453 |