EVENT DETAILS AND ABSTRACT

Title: Potential Automorphy for $GL_n$
Speaker: Lie Qian
Speaker Info: Stanford University
Brief Description:
Special Note:
Abstract:

Abstract: We prove that under mild condition for the residual representation, any ordinary $l$-adic representation of the absolute Galois group $G_F$ of a CM number field $F$ can be made automorphic when restricted to some subgroup $G_{F'}$. The result gives a much larger class of potential automorphic Galois representation than previously known in the sense that most previous results works with groups like $GSp_n$, or a compatible family of Galois representation. The family of Dwork motives is the main object we study. Along the way, we also prove an interesting ordinarity result concerning the cohomologies (viewed as local $p$-adic Galois representation) associated to certain fibres of that family.