# Le lemme fondamental pour les algebres de Lie

@article{Chu2008LeLF, title={Le lemme fondamental pour les algebres de Lie}, author={Ng{\^o} Bao Ch{\^a}u}, journal={arXiv: Algebraic Geometry}, year={2008} }

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.

## 257 Citations

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

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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

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- 2016

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…

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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…

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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

- Mathematics
- 2014

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

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- 2022

. 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

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- 2021

: 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

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- 2016

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

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- 2019

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

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- 2011

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…

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