2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67410We show that Ax-Katz divisibility on the number of rational points of a variety defined over a finite field by equations of low degrees comes from divisibility of the eigenvalues of the Frobenius action of the $\ell$-adic cohomology with compact supports. This completes the motivc picture, as we knew already that in characteristic 0, the Hodge type was the expected one. [version 2 as the title contained a typo..., else no changes]10 pages, latexNumber TheoryAlgebraic Geometrytext