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.
"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