Eisenstein intersection points on the Hilbert Eigenvariety

Abstract: In this talk, we will report a joint work with M. Dimitrov and S.C. Shih in which we study the local geometry of the Hilbert Eigenvariety at an intersection point between an Eisenstein component and the cuspidal locus. As applications, we show the non-vanishing of certain Katz $p$-adic $L$-functions at $s=0$ and give a new proof of the Gross-Stark conjecture in the rank one case.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic