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首页> 外文期刊>Annales scientifiques de l'Ecole normale superieure >THE HITCHIN-FRENKEL-NGO FIBRATION AND ITS INTERSECTION COMPLEX
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THE HITCHIN-FRENKEL-NGO FIBRATION AND ITS INTERSECTION COMPLEX

机译：Hitchin-Frenkel-Ngo振动及其交叉口复合物

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In this article, we construct the Hitchin fibration for groups following the scheme outlined by Frenkel-Ngo [14] in the case of SL2. This construction uses as a decisive tool the Vinberg semigroup and follows the study accomplished in [4]. The total space of Hitchin is obtained by taking the fiber product of the Hecke stack with the diagonal of the stack of G-bundles Bun(G); we prove a transversality statement between the intersection complex of the Hecke stack and the diagonal of BunG, over a sufficiently big open subset, in order to get local applications, such as the fundamental lemma for the spherical Hecke algebra. Along the proof of this theorem, we establish a result concerning the integral conjugacy classes of the points of a simply connected group in a local field.
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