Le lemme fondamental pour les groupes unitaires

By G. Laumon, B. Ngô. 2004

109 citations recorded by the source corpus.

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 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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d7e281273eba521ce7ffb11c24882652f805853a

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In Discrete Mathematics and Combinatorics

1. C. Moeglin
2. J. Arthur
3. Robert D. MacPherson
4. Mark Goresky
5. N. Châu
6. Zhiwei Yun
7. R. Kottwitz
8. I. Leary

In Geometry and Topology

1. Zhiwei Yun
2. N. Châu
3. J. Arthur
4. Robert D. MacPherson
5. Mark Goresky
6. C. Moeglin
7. R. Kottwitz
8. Tasho Kaletha

In Mathematical Physics

1. Zhiwei Yun
2. N. Châu
3. J. Arthur
4. C. Moeglin
5. Robert D. MacPherson
6. Mark Goresky
7. R. Kottwitz
8. Tasho Kaletha

Citations in the corpus

• Classification et changement de base pour les séries discrètes des groupes unitaires p-adiques (2006, background): “Les premi`eres hypoth`eses sont disponibles grˆace `a [10] [24] et [21].”
• Homology of affine Springer fibers in the unramified case (2003, methodology): “ich we have not fully carried out here. In §15.12 we indicate how these results are related to the fundamental lemma in the unramified case. We would also like to draw attention to the recent preprint [L02a] in which G. Laumon uses the methods and techniques of the present paper together with a defor”
• A Note on L-packets (2006, background): “Recently, Laumon and Ngo [LN] and Waldspurger [W2] have established the fundamental lemma for unitary groups.”
• The fundamental lemma of Jacquet and Rallis (2011, background): “The geometry of Hitchin fibrations is studied in great detail by Ngô [12] and Laumon-Ngô [10]; the latter treats the unitary group case, which is especially important for the purpose of this article.”
• Le lemme fondamental pour les algebres de Lie (2008, background): “3 de [54] que nous allons maintenant rappeler et généraliser légèrement.”
• Constructible exponential functions, motivic Fourier transform and transfer principle (2005, unknown): “In this direction, we mention work by Cunningham and Hales [13], and recall that the Fundamental Lemma over functions fields has been proved by Laumon and Ngô for unitary groups [25] and more recently by Ngô for Lie algebras [27], and that Waldspurger deduced the case of p-adic fields [33] by repres”