Fibration de Hitchin et endoscopie

Details Fibration de Hitchin et endoscopie Fibration de Hitchin et endoscopie

2004-06-29

arxiv.org/abs/math/0406599v4

Invent. Math. 164 (2006), no. 2, 399--453

Mathematics

Algebraic Geometry

published version, Latex file

Scientific paper

We propose a geometric interpretation of the theory of elliptic endoscopy, due to Langlands and Kottwitz, in terms of the Hitchin fibration. As applications, we prove a global analog of a purity conjecture, due to Goresky, Kottwitz and MacPherson. For unitary groups, this global purity statement has been used, in a joint work with G. Laumon, to prove the fundamental lemma over local fields of equal characteristics.

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