Abstract
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.
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Ngô, B. Fibration de Hitchin et endoscopie. Invent. math. 164, 399–453 (2006). https://doi.org/10.1007/s00222-005-0483-7
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DOI: https://doi.org/10.1007/s00222-005-0483-7