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arXiv · 2202.03303

Serre weights for three-dimensional wildly ramified Galois representations

Daniel Le·Bao Viet Le Hung·Brandon Levin·Stefano Morra
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Abstract

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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Daniel Le, Bao Viet Le Hung, Brandon Levin, Stefano Morra. 2022-02-07. Serre weights for three-dimensional wildly ramified Galois representations. https://doi.org/10.2140/ant.2024.18.1221

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