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

Includes index and bibliography

The orthogonal Shimura varieties -- Definition of the terms in Morel’s formula -- Proof of Morel’s formula -- Comparison with discrete series characters -- Endoscopic data for special orthogonal groups -- Transfer factors for real special orthogonal groups -- Transfer maps defined by the Satake isomorphism -- Stabilization -- Application: spectral expansion and Hasse–Weil zeta functions

The author studies Shimura varieties associated with special orthogonal groups over the field of rational numbers. He proves a version of Morel's formula for the Frobenius-Hecke traces on the intersection cohomology of the Baily-Borel compactification. His main result is the stabilization of this formula. As an application, he computes the Hasse-Weil zeta function of the intersection cohomology in some special cases, using the recent work of Arthur and Taïbi on the endoscopic classification of automorphic representations of special orthogonal groups.