Arithmetic level raising for GSp(4)

Level raising theorems for modular forms are theorems about congruences of modular forms between different levels. These theorems play an important role in the proof of the Fermat’s last theorem by Wiles. In this talk, we will report some recent work on realizing level raising theorems for automorphic forms on GSp(4) by studying the geometry of certain quaternionic unitary Shimura variety.