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Serre weights for
three-dimensional wildly ramified Galois representations
Daniel Le, Bao V. Le Hung, Brandon Levin and Stefano Morra |
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Vol. 18 (2024), No. 7, 1221–1274
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DOI: 10.2140/ant.2024.18.1221
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Abstract |
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We formulate and prove the weight part of Serre’s conjecture for three-dimensional mod Galois representations under a genericity condition when the field is unramified at . This removes the assumption made previously that the representation be tamely ramified at . We also prove a version of Breuil’s lattice conjecture and a mod multiplicity one result for the cohomology of -arithmetic manifolds. The key input is a study of the geometry of the Emerton–Gee stacks using the local models we introduced previously (2023). |
Keywords
weight part of Serre's conjectures, local models for Galois
representations, mod $p$ cohomology of arithmetic
manifolds, congruences of automorphic forms
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Mathematical Subject Classification
Primary: 11F33, 11F80, 22E50
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Milestones
Received: 9 February 2022
Revised: 21 April 2023
Accepted: 3 September 2023
Published: 13 June 2024
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Authors |
| Daniel Le | |
| Department of Mathematics Purdue University West Lafayette, IN United States |
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| Bao V. Le Hung | |
| Department of Mathematics Northwestern University Evanston, IL United States |
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| Brandon Levin | |
| Department of Mathematics Rice University Houston, TX United States |
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| Stefano Morra | |
| Laboratoire Analyse Géométrie
Applications Université Paris 8 Villetaneuse France |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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