Potentially crystalline deformation rings and Serre weight conjectures

2015/12/20 by Daniel Le, Le, Daniel, Bao V. Le Hung +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1512.06380

openalex publication_date 2015/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the weight part of Serre's conjecture in generic situations for forms of U(3) which are compact at infinity and split at places dividing p as conjectured by Herzig. We also prove automorphy lifting theorems in dimension three. The key input is an explicit description of tamely potentially crystalline deformation rings with Hodge-Tate weights (2,1,0) for K/ℚ_p unramified combined with patching techniques. Our results show that the (geometric) Breuil-Mézard conjectures hold for these deformation rings.

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