Deformation of Rigid Conjugate Self-dual Galois Representations  

作　　者：Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen ZHU 

机构地区：[1]Institute for Advanced Study in Mathematics,Zhejiang University,Hangzhou 310058,P.R.China [2]Morningside Center of Mathematics,AMSS,Chinese Academy of Sciences,Beijing 100190,P.R.China [3]New Cornerstone Lab,Beijing International Center for Mathematical Research,Peking Ui Beijing 100871,P.R.China [4]Department of Mathematics,Massachusetts Institute of Technology,Cambridge MA 02139,United States [5]Department of Mathematics,Stanford University,Stanford,CA 94305,United States

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1599-1644,共46页数学学报（英文版）

基　　金：Y.L.supported by NSF(Grant No.DMS-1702019)and a Sloan Research Fellowship;Y.T.supported by NSFC(Grant No.12225112/12231001);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 Education;W.Z.supported by NSF(Grant No.DMS-1838118/DMS-1901642);X.Z.supported by NSF(Grant No.DMS-1902239)and a Simons Fellowship。

摘　　要：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.

关 键 词：Galois deformation rigid conjugate self-dual Galois representations 

分 类 号：O15[理学—数学]