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Pré-Publication, Document De Travail Année : 2022

Serre weights for three-dimensional wildly ramified Galois representations

Résumé

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}.
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Dates et versions

hal-03840804 , version 1 (06-11-2022)

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Daniel Le, Bao Viet Le Hung, Brandon Levin, Stefano Morra. Serre weights for three-dimensional wildly ramified Galois representations. 2022. ⟨hal-03840804⟩
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