2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126380For a linear group $G$ acting on an absolutely irreducible variety $X$ over the rationals $\QQ$, we describe the orbits of $X(\QQ_p)$ under $G(\QQ_p)$ and of $X(\FF_p((t)))$ under $G(\FF_p((t)))$ for $p$ big enough. This allows us to show that the degree of a wide class of orbital integrals over $\QQ_p$ or $\FF_p((t))$ is $\leq 0$ for $p$ big enough, and similarly for all finite field extensions of $\QQ_p$ and $\FF_p((t))$.Algebraic GeometryLogicNumber Theory11S40, 03C98; 22E35, 11S20text