2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78382The purpose of this paper is to give an explicit formula which allows one to compute the dimension of the cohomology groups of the sheaf $Ω_¶^p(D)$ of p-th differential forms of Zariski twisted by an ample invertible sheaf on a complete simplicial toric variety. The formula involves some combinatorial sums of integer points over all faces of the support polytope for ${Ø_X}(D)$. We also introduce a new combinatorial object, the so-called p-th Hilbert-Erhart polynomial, which generalizes the usual notion and behaves similar. Namely, there exists a generalization of the inversion law for a usual Hilbert-Erhart polynomial. Some applications of the Bott formula are discussed.18 pages, LaTeX 2e, no figures. Revised versionAlgebraic Geometry14M25, 32L10, 58A10text