题目：Big images of Galois representations associated to Hida families
摘要：We study the images of Galois representations associated to Hida families. In 2015, Hida and Jacyln Lang have proved that the image of Galois 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 finite extension of this algebra, which is called the self-twist ring. Hida and Tilouine have proved similar results in the case of Hida families of “general” Siegel modular forms of genus 2. Under some technical hypothesis, we have generalized the results to the case of general reductive groups, when the associated Galois representations exist. In this talk, I will explain the results and show the main steps of the proof.