2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140315Let $X_Σ$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $Σ$, computes the integral cohomology of $X_Σ$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_Σ$ is formal.10 pagesAlgebraic TopologyAlgebraic Geometry14M25, 55N10 (primary), 14C15, 55N91 (secondary)text