On the automorphy of 2-dimensional potentially semi-stable deformation rings of G_ℚp

2018/03/19 by Shen-Ning Tung, Tung, Shen-Ning · 3 citations
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1803.07451

Abstract

Using p-adic local Langlands correspondence for GL₂(ℚ_p), we prove that the support of patched modules constructed by Caraiani, Emerton, Gee, Geraghty, Paskunas, and Shin meet every irreducible component of the potentially semistable deformation ring. This gives a new proof of the Breuil-Mézard conjecture for 2-dimensional representations of the absolute Galois group of ℚ_p when p > 2, which is new in the case p = 3 and r a twist of an extension of the trivial character by the mod p cyclotomic character. As a consequence, a local restriction in the proof of Fontaine-Mazur conjecture by Kisin is removed.

Citations

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings

Cited by

• Finiteness properties of the category of mod p representations of\n \GL₂(\ℚ_p)
• On the finite length of some p-adic representations of the quaternion algebra over \Q_p
• Infinitesimal characters in arithmetic families

Related

• On 2-adic deformations
• Potentially semi-stable deformation rings for representations with values in PGL_n
• Irreducible components of deformation spaces: wild 2-adic exercises
• Un calcul d'anneaux de déformations potentiellement Barsotti--Tate
• Local models for Galois deformation rings and applications