2004/04/26 by Gérard Laumon, G. Laumon, Laumon, G. +3 · 4 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.AG #math.RT #msc:14F20 #msc:14H60 #msc:22E35
paper · pdf · doi:10.48550/arxiv.math/0404454
99 pages, Plain TeX file. New propositions 2.5.2 and 2.8.4. New lemma 3.2.5. Section (3.4) completely rewritten. Argument on pages 84-85 corrected. Chapter 3 simplified by restricting to the case I={1,2}. References [Fal], [F-G-S] and [Hal] added. Minor additional changes
Let G be an unramified reductive group over a non archimedian local field F. The so-called "Langlands Fundamental Lemma" is a family of conjectural identities between orbital integrals for G(F) and orbital integrals for endoscopic groups of G. In this paper we prove the Langlands fundamental lemma in the particular case where F is a finite extension of Fp((t)), G is a unitary group and p>rank(G). Waldspurger has shown that this particular case implies the Langlands fundamental lemma for unitary groups of rank <p when F is any finite extension of Qp. We follow in part a strategy initiated by Goresky, Kottwitz and MacPherson. Our main new tool is a deformation of orbital integrals which is constructed with the help of the Hitchin fibration for unitary groups over projective curves.