Fundamental lemma for unitary groups

• 成果类型: Article
• 署名作者: Laumon, Gerard; Ngo, Bao Chau
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.168.477
• 发表日期: 2008
• 页码: 477-573
• 关键词: curves; VARIETIES

摘要

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 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 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.