Speaker: Dr. Huan Chen
Time: 9:00-10:00, Dec 03, 2020 (Beijing Time)
Abstract: We study the images of Galois representations associated to Hida families. In 2015, Hida and Jacyln Lang have proved that the image of Ga-lois representation associated to a non-CM family of ordinary classical modular forms contains a congruence subgroup of Iwasawa algebra of weights and also of a nite extension of this algebra, which is called the self-twist ring. Hida and Jacques Tilouine have generalized the results about the existence of nontrivial congruence subgroups contained in the image of the Galois representation to the case of a Hida family of "general" Siegel modular forms of genus 2. Under some technical hypothesis, we have proved the same result for general reductive groups, when the associated Galois representation exists. In this talk, I will explain the results and show the main steps of the proof. This is a joint work with Jacques Tilouine.