2020/06/08 by Spencer Leslie, Leslie, Spencer
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2006.04993
openalex publication_date 2020/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the study of periods of automorphic forms and relative trace\nformulae, we develop the theory of descent necessary to study orbital integrals\narising in the fundamental lemma for a general class of symmetric spaces over a\np-adic field F. More precisely, we prove that a connected symmetric space\nover F enjoys a notion of topological Jordan decomposition, which may be of\nindependent interest, and establish a relative version of a lemma of Kazhdan\nthat played a crucial role in the proof of the Langlands-Shelstad fundamental\nlemma.\n As our main application, we use these results to prove the endoscopic\nfundamental lemma for the unit element of the Hecke algebra for the symmetric\nspace associated to unitary Friedberg-Jacquet periods.\n