Yichao TIAN will speak on

On the super-singular locus of Hilbert modular varieties and arithmetic applications

Abstract:We will study the super-singular locus of odd dimensional Hilbert modular varieties at an inert prime. The main result says that the super-singular locus is an iterated P^1 bundle over a zero-dimensional Shimura variety associated to a definite quaternion algebra. This has some applications to congruences of Hilbert modular forms, which can be viewed as an analogue of Ribet classical theorem on level raising of modular forms. This is a joint work in progress with Y. Liu and L. Xiao.