2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66031This is meant to be a survey article for the Cubo Journal. We discuss the existence and number of rational points over a finite field, the Hodge type over the complex numbers, and the motivic conjectures which are controlling those invariants. We present a geometric version of it.11 pagesAlgebraic GeometryCongruences for the number of rational points, Hodge type and motivic conjectures for Fano varietiestext