In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite...In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.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.展开更多
基金Y.L.supported by NSF(Grant No.DMS-1702019)and a Sloan Research FellowshipY.T.supported by NSFC(Grant No.12225112/12231001)+4 种基金CAS Project for Young Scientists in Basic Research(Grant No.YSBR-033)L.X.supported by NSF(Grant No.DMS-1502147/DMS-1752703)NSFC(Grant No.12071004)and the Chinese Ministry of EducationW.Z.supported by NSF(Grant No.DMS-1838118/DMS-1901642)X.Z.supported by NSF(Grant No.DMS-1902239)and a Simons Fellowship。
文摘In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.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.
