Espaces FC(g(F)) et endosopie = FC(g(F)) spaces and endoscopy / Jean-Loup Waldspurger

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Summary language: French, English Series: Mémoires de la Société Mathématique de France ; nouvelle série, numéro 187Publisher: Paris : Société mathématique de France, 2025Description: 1 Online-Ressource (vii, 148 Seiten)Other title:
  • FC(g(F)) spaces and endoscopy
Subject(s): Additional physical formats: 9782379052187 | Erscheint auch als: Espaces FC(g(F)) et endosopie. Druck-Ausgabe Paris : Société mathématique de France, 2025. vii, 148 SeitenMSC: MSC: 22E50RVK: RVK: SK 340DOI: DOI: 10.24033/msmf.493Online resources: Summary: Mots Clés: Transfert endoscopique, stabilité, faisceaux-caractères, éléments topologiquement nilpotentsSummary: Keywords: Endoscopic transfer, stability, character-sheaves, topologically nilpotent elementsSummary: Let F be a p-adic field and let G be a connected reductive group defined over F. We assume p is large. Denote by g the Lie algebra of G. We normalize suitably a Fourier-transform f↦f^ on C∞c(g(F)). In a preceeding paper, we have defined the space FC(g(F)) of functions f∈C∞c(g(F)) such that the orbital integrals of f and of f^ are 0 for each element of g(F) which is not topologically nilpotent. These spaces are compatible with endoscopic transfer. We assume here that G is absolutely quasi-simple and simply connected. We define a decomposition of the space FC(g(F)) in a direct sum of subspaces such that the endoscopic transfer becomes (more or less) clear on each subspace. In particular, if G is quasi-split, we describe the subspace FCst(g(F)) of ‘stable” elements in FC(g(F)).PPN: PPN: 1939508258
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