Le lemme fondamental pour les algebres de Lie

By N. Châu. 2008

277 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d9e330d580109f21e26a7e09051c16db579bde96

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, methodology): “The paper [152] is devoted to the proof of the fundamental lemma in the Langland’s program, a long-standing and deep conjecture concerning Lie groups.”
Epipelagic $$L$$L-packets and rectifying characters (2012, methodology): “The proof of these two theorems is based on the work of Adler and Spice [3] on the characters of supercuspidal representations, the works of Waldspurger [55,56], and Ngo [46] on endoscopy for p-adic Liealgebras, as well as a recent result of Kottwitz on the comparison ofWeil constants and epsilon fa”
On Mœglin's Parametrization of Arthur Packets for p-adic Quasisplit Sp (N) and SO(N) (2015, background): “Finally it is in this particular form of the fundamental lemma, Ngo [Ngô10] gave his celebrated proof.”
Geometric representations of graded and rational Cherednik algebras (2014, methodology): “Ngô’s original definition uses the action of π0(Pa) instead of X∗(T), and is in fact equivalent to our definition because of the following lemma.”
Families of L -Functions and Their Symmetry (2014, methodology): “An interesting feature of their proof is that it uses the function field analogues to verify the identities and in this sense it is similar to the recent proof of the Fundamental Lemma ([80] and references therein).”
Torus knots and the rational DAHA (2012, methodology): “[Ngo10] B-C.”
Global Springer theory (2011, methodology): “1], we have the following product formula, whose proof is identical with the case of Hitchin fibers in [29].”
Level raising and symmetric power functoriality, II (2015, background): “…for the precise identity, and we only note that all the terms are now well defined due to the proof of the fundamental lemma for units of the Hecke alge- bra [CL10], [CL12], [Ngô10], [Wal09a], [Wal09b] (implying, by Waldspurger’s work [Wal97], the corresponding transfer of smooth functions).”
Transfer Principle for the Fundamental Lemma (2007, background): “[25] G. Laumon, B. C. Ngô, Le lemme fondamental pour les groupes unitaires, math.”