2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79465Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. We show that if X is Frobenius split then so is the Hilbert scheme Hilb^n(X) of n points in X. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb^n(X) when X is projective and Frobenius split.Latex, 12 pagesAlgebraic Geometrytext