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 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 defined over the residual field . We normalize suitably a Fourier-transform on . We study the subspace of functions such that the orbital integrals of f and of are 0 for each element of which is not topologically nilpotent. This space is related to the characteristic functions of the character-sheaves on the spaces , for each vertex s, which are cuspidal and with nilpotent support. We prove that our subspace behave well under endoscopy.
Citation
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