CM points on compact orthogonal groups and theta lifts mod $p$

Abstract: CM points on Shimura varieties are very useful in the study of arithmetic properties of automorphic forms, $L$-functions, etc.. C. Cornut and V. Vatsal proved certain dynamical properties of these points on quaternions and then deduce Mazur's conjectures as well as study the non-vanishing of Rankin-Selberg $L$-values. In this talk we try to follow the strategy of Cornut and Vatsal and generalise their result to certain compact orthogonal groups and as an application, we study the non-vanishing problem of theta lifts mod $p$ from orthogonal group to symplectic group.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar