Selmer groups and arithmetic geometry of Shimura varieties

In this talk, we will introduce some recent progress on the Bloch-Kato conjecture, which relates L-functions and Selmer groups of motives, generalizing the BS-D conjecture. We will explain how the study of integral models of Shimura varieties can help to understand the size of Selmer groups, and how L-functions are encoded in the arithmetic geometry of Shimura varieties.​