Serre weights for three-dimensional wildly ramified Galois representations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910492431220736 |
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| author | Le, Daniel Hung, Bao Viet Le Levin, Brandon Morra, Stefano |
| author_facet | Le, Daniel Hung, Bao Viet Le Levin, Brandon Morra, Stefano |
| contents | We formulate and prove the weight part of Serre's conjecture for three-dimensional mod $p$ Galois representations under a genericity condition when the field is unramified at $p$. This removes the assumption in \cite{arXiv:1512.06380}, \cite{arXiv:1608.06570} that the representation be tamely ramified at $p$. We also prove a version of Breuil's lattice conjecture and a mod $p$ multiplicity one result for the cohomology of $U(3)$-arithmetic manifolds. The key input is a study of the geometry of the Emerton--Gee stacks \cite{arXiv:2012.12719} using the local models introduced in \cite{arXiv:2007.05398}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03303 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Serre weights for three-dimensional wildly ramified Galois representations Le, Daniel Hung, Bao Viet Le Levin, Brandon Morra, Stefano Number Theory Algebraic Geometry Representation Theory 11F80, 11F33, We formulate and prove the weight part of Serre's conjecture for three-dimensional mod $p$ Galois representations under a genericity condition when the field is unramified at $p$. This removes the assumption in \cite{arXiv:1512.06380}, \cite{arXiv:1608.06570} that the representation be tamely ramified at $p$. We also prove a version of Breuil's lattice conjecture and a mod $p$ multiplicity one result for the cohomology of $U(3)$-arithmetic manifolds. The key input is a study of the geometry of the Emerton--Gee stacks \cite{arXiv:2012.12719} using the local models introduced in \cite{arXiv:2007.05398}. |
| title | Serre weights for three-dimensional wildly ramified Galois representations |
| topic | Number Theory Algebraic Geometry Representation Theory 11F80, 11F33, |
| url | https://arxiv.org/abs/2202.03303 |