The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varieties

Yihang Zhu

Published 2018-01-29Version 1

The orthogonal Shimura varieties are associated to special orthogonal groups over $\mathbb Q$ of signature $(n,2)$ at infinity. We consider the intersection cohomology of their Baily--Borel compactifications, and prove a version of Morel's formula for the Frobenius--Hecke traces on it for almost all primes. Our main result is the stabilization of this formula. As an application, we compute the Hasse--Weil zeta function of the intersection cohomology in some special cases, using the recent work of Arthur and Ta\"ibi on the endoscopic classification of automorphic representations of special orthogonal groups.