Le, DanielLe Hung, Bao V.Levin, BrandonMorra, Stefano2024-10-082024-10-082024Le, D., Le Hung, B. V., Levin, B., & Morra, S. (2024). Serre weights for three-dimensional wildly ramified Galois representations. Algebra & Number Theory, 18(7), 1221–1274. https://doi.org/10.2140/ant.2024.18.1221https://hdl.handle.net/1911/117915We 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 made previously 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 using the local models we introduced previously (2023).engExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license. Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Journal articleant-v18-n7-p01-shttps://doi.org/10.2140/ant.2024.18.1221