Le lemme fondamental pour les groupes unitaires

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dc.creatorLaumon, G.
dc.creatorNgo, B. C.
dc.date2004-04-26
dc.date2004-10-08
dc.date.accessioned2026-07-07T05:07:43Z
dc.date.available2026-07-07T05:07:43Z
dc.descriptionLet 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 F_p((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 Q_p. 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.
dc.description99 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
dc.identifierhttps://arxiv.org/abs/math/0404454
dc.identifierhttp://arxiv.org/abs/math/0404454
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70966
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14H60, 22E35 (Primary) 14F20 (Secondary)
dc.titleLe lemme fondamental pour les groupes unitaires
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