2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227213Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer coefficients. Moreover, the shifted periodic polynomial function, where $q^n$ is formally replaced with $q^n + 1$, is shown to have non-negative coefficients.Algebraic Geometry13A50, 14G15, 14L30, 14M17text