The fundamental lemma of Jacquet-Rallis in positive characteristics

Abstract

We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is greater than the rank of the relevant groups.

40 pages; Both the group Version and the Lie algebra version are proved

References in corpus (3)

• Constructible motivic functions and motivic integration
• Le lemme fondamental pour les groupes unitaires
• Fibration de Hitchin et endoscopie

Cited by in corpus (12)

• On the Arithmetic Fundamental Lemma in the minuscule case
• On the arithmetic transfer conjecture for exotic smooth formal moduli spaces
• Integrability of oscillatory functions on local fields: transfer principles
• Whittaker periods, motivic periods, and special values of tensor product L-functions
• Arithmetic diagonal cycles on unitary Shimura varieties
• The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods
• Isolation of cuspidal spectrum, with application to the Gan--Gross--Prasad conjecture
• Shtukas and the Taylor expansion of $L$-functions
• Endoscopic transfer for unitary Lie algebras
• Regular formal moduli spaces and arithmetic transfer conjectures
• Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
• Automorphic Forms on Unitary Groups