Thursday, November 8, 2018
Number Theory Seminar
Slopes in eigenvarieties for definite unitary groups
Lynnelle Ye, Department of Mathematics, Harvard University
The study of eigenvarieties began with Coleman and Mazur, who constructed the first eigencurve, a rigid analytic space whose points are in bijection with $p$-adic modular Hecke eigenforms. Since then various authors have constructed eigenvarieties for automorphic forms on many other groups. We will state a structure theorem about Chenevier's eigenvarieties for definite unitary groups which generalizes slope bounds of Liu-Wan-Xiao for dimension $2$ to all dimensions. We will then discuss the ideas of the proof, which goes through the classification of automorphic representations that are principal series at $p$, and a geometric consequence.