Deformation of rigid conjugate self-dual Galois representations

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.

arXiv comment42 pages. This article is essentially the original Appendix E of the article arXiv:1912.11942; we now decide to make that appendix an independent article

References in corpus (5)

• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• On the automorphy of $l$-adic Galois representations with small residual image
• G-valued local deformation rings and global lifts
• Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations
• The Breuil--Mézard conjecture for function fields