Germ expansion, endoscopic transfer, and unitary periods

Abstract

In this thesis, we study the germ expansions in the Jacquet-Rallis transfer. We prove an identity that relates certain nilpotent orbital integrals for any smooth matching in this transfer. We give two applications of this identity. For the first, we give an elementary local proof of the endoscopic fundamental lemma for unitary groups (theorem of Laumon and Ngo). For the second, we establish a new relative trace formula comparison conjectured by Jacquet that can be used to study unitary periods.