Fibration de Hitchin et endoscopie
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- Ngô, B. Invent. math. (2006) 164: 399. doi:10.1007/s00222-005-0483-7
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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 a local fields of equal characteristics.