La fibration de Hitchin-Frenkel-Ngo et son complexe d'intersection

2014/09/03 by Bouthier, Alexis
#Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.1275

Abstract

In this article, we construct the Hitchin fibration for groups following the scheme outlined by Frenkel-Ngo in the case of SL₂. This construction uses as a decisive tool the Vinberg's semigroup. 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 Bun_G, over a sufficiently big open subset, in order to get local applications, such that 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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