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August 2022 Fonctions Dont les Intégrales Orbitales et Celles de Leurs Transformées de Fourier Sont à Support Topologiquement Nilpotent
J.-L. Waldspurger
Michigan Math. J. 72: 621-641 (August 2022). DOI: 10.1307/mmj/20207203

Abstract

Let F be a p-adic field and let G be a connected reductive group defined over F. We assume p is large. 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 gs defined over the residual field Fq. We normalize suitably a Fourier-transform ffˆ on Cc(g(F)). We study the subspace of functions fCc(g(F)) such that the orbital integrals of f and of fˆ are 0 for each element of g(F) which is not topologically nilpotent. This space is related to the characteristic functions of the character-sheaves on the spaces gs(Fq), for each vertex s, which are cuspidal and with nilpotent support. We prove that our subspace behave well under endoscopy.

Citation

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J.-L. Waldspurger. "Fonctions Dont les Intégrales Orbitales et Celles de Leurs Transformées de Fourier Sont à Support Topologiquement Nilpotent." Michigan Math. J. 72 621 - 641, August 2022. https://doi.org/10.1307/mmj/20207203

Information

Received: 8 November 2020; Revised: 30 May 2021; Published: August 2022
First available in Project Euclid: 2 August 2022

Digital Object Identifier: 10.1307/mmj/20207203

Subjects:
Primary: 22E35
Secondary: 22E50

Rights: Copyright © 2022 The University of Michigan

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Vol.72 • August 2022
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