Deformation of rigid conjugate self-dual Galois representations

2021/08/16 by Yifeng Liu, Yichao Tian, Liu, Yifeng +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2108.06998

openalex publication_date 2021/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.

Citations

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
• The Breuil--Mézard conjecture for function fields

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• Survey on bounding Selmer groups for Rankin--Selberg motives

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