• Corpus ID: 115166363

Le lemme fondamental pour les algebres de Lie

  title={Le lemme fondamental pour les algebres de Lie},
  author={Ng{\^o} Bao Ch{\^a}u},
  journal={arXiv: Algebraic Geometry},
  • N. Châu
  • Published 3 January 2008
  • Mathematics
  • arXiv: Algebraic Geometry
We propose a proof for conjectures of Langlands, Shelstad and Waldspurger known as the fundamental lemma for Lie algebras and the non-standard fundamental lemma. The proof is based on a study of the decomposition of the l-adic cohomology of the Hitchin fibration into direct sum of simple perverse sheaves. 

Le lemme fondamental pond\'er\'e. II. \'Enonc\'es cohomologiques

In this paper, we study the cohomology of the truncated Hitchin fibration, which was introduced in a previous paper. We extend Ng\^o's main theorems on the cohomology of the elliptic part of the

A support theorem for the Hitchin fibration: the case of

We prove that the direct image complex for the $D$-twisted $SL_n$ Hitchin fibration is determined by its restriction to the elliptic locus, where the spectral curves are integral. The analogous

The decomposition theorem, perverse sheaves and the topology of algebraic maps

We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the

Descent Construction for GSpin Groups

In this paper we provide an extension of the theory of descent of Ginzburg-Rallis- Soudry to the context of essentially self-dual representations, that is representations which are isomorphic to the

Un th\'eor\`eme du support pour la fibration de Hitchin

The main tool in Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad fundamental lemma, is a theorem on the support of the relative cohomology of the elliptic part of the Hitchin fibration. For GL(n)

Hodge-to-singular correspondence for reduced curves

. We study the summands of the decomposition theorem for the Hitchin system for GL n , in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between

Faisceaux caract\`eres sur les espaces de lacets d'alg\`ebres de Lie

: We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and its

The Local Langlands Conjectures for Non-quasi-split Groups

We present different statements of the local Langlands conjectures for non-quasi-split groups that currently exist in the literature and provide an overview of their historic development. Afterwards,

Motivic Integration on the Hitchin Fibration

We prove that the moduli spaces of twisted $\mathrm{SL}_n$ and $\mathrm{PGL}_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow

Global topology of the Hitchin system

Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic



Le lemme fondamental pour les groupes unitaires

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

Homology of affine Springer fibers in the unramified case

Assuming a certain “purity” conjecture, we derive a formula for the (complex) cohomology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this

Théorèmes de connexité pour les produits d'espaces projectifs et les Grassmanniennes

We give a numerical condition on the images of two morphisms to a Grassmannian (or a product of projective spaces) that ensures that their fibered product is connected, thereby extending

Codimensions of root valuation strata

This paper defines and studies a stratification of the adjoint quotient of the Lie algebra of a reductive group over a Laurent power series field. The stratification arises naturally in the context

Algebraic loop groups and moduli spaces of bundles

Abstract.We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine


Consider a connected reductive group G over a number field F. For technical reasons we assume that the derived group of G is simply connected (see [L1]). in [L3] Langlands partially stabilizes the

Euler number of the compactified Jacobian and multiplicity of rational curves

We show that the Euler number of the compactified Jacobian of a rational curve $C$ with locally planar singularities is equal to the multiplicity of the $\delta$-constant stratum in the base of a

Base change for unit elements of Hecke algebras

© Foundation Compositio Mathematica, 1986, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions

Some Basic Theorems on Algebraic Groups

The subject of algebraic groups has had a rapid development in recent years. Leaving aside the late research by many people on the Albanese and Picard variety, it has received much substance and