Fonctions dont les intégrales orbitales et celles de leurs transformées de Fourier sont à support topologiquement nilpotent
Résumé
Let F be a p-adic field and let G be a connected reductive group defined over F. We assume p is big. Denote g the Lie algebra of G. To each vertex s of the reduced Bruhat-Tits' building of G, we associate as usual a reductive Lie algebra g_s defined over the residual field F_q. We normalize suitably a Fourier-transform f →^f on the space of functions on g(F). We study the subspace of functions f such that the orbital integrals of f and of ^f are 0 for each element of g(F) which is not topologically nilpotent. It is related to the characteristic functions of the character-sheaves on g_s(F_q), for each s, which are cuspidal and with nilpotent support. We prove that our subspace behave well under endoscopy.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...