Chi-Yun Hsu, Harvard

Title:Ramification of Hilbert eigenvarieties at classical points

Abstract: A p-adic modular form is a p-adic limit of modular forms in terms of q-expansions. The eigencurve, introduced by Coleman and Mazur, is a geometric object parametrizing p-adic Hecke eigenforms which are finite-slope and overconvergent. It admits a map to the weight space, sending an eigenform to its weight. When the Hecke action is not semisimple, the eigencurve ramifies over the weight space. We give a characterization of the classical ramification points in terms of their associated Galois representation. This generalizes to eigenvarieties for Hilbert modular forms.