TY  - BOOK
AU  - Zhu,Yihang
TI  - The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties
T2  - Asterisque
SN  - 9782379052033
U1  - 514.23 23rd
PY  - 2024///
CY  - Marseille
PB  - Société Mathématique de France
KW  - Number Theory
KW  - Algebraic Geometry
KW  - Representation Theory
N1  - 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
N2  - 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
ER  -