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Medientyp:
E-Artikel
Titel:
Le Lemme Fondamental Pour Les Groupes Unitaires
Beteiligte:
Laumon, Gérard;
Ngô, Bao Châu
Erschienen:
Princeton University Press, 2008
Erschienen in:
Annals of Mathematics, 168 (2008) 2, Seite 477-573
Sprache:
Englisch
ISSN:
0003-486X
Entstehung:
Anmerkungen:
Beschreibung:
<p>Let G be an unramified reductive group over a nonarchimedian 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 endoscopie 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.</p>