  We 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]
