Crystalline extensions and the weight part of Serre's conjecture

2011/06/28 by Toby Gee, Tong Liu, Gee, Toby +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1106.5584

openalex publication_date 2011/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p>2 be prime. We complete the proof of the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the totally ramified case, by proving that any weight which occurs is a predicted weight. Our methods are a mixture of local and global techniques, and in the course of the proof we establish some purely local results on crystalline extension classes.

Related

• The Buzzard-Diamond-Jarvis conjecture for unitary groups
• Serre weights for rank two unitary groups
• Serre Weights for U(n)
• The weight part of Serre's conjecture for GL(2)
• Extremal weights and a tameness criterion for mod p Galois representations