The weight part of Serre's conjecture for GL(2)

2013/09/02 by Toby Gee, Tong Liu, Gee, Toby +3
Mathematics · #11F33 #11F80 #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.1309.0527

openalex publication_date 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate representations", over arbitrary finite extensions of the p-adics. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.

Citations

• Lattices in the cohomology of Shimura curves

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