2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227781Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X. This establishes part of the Homological Mirror Conjecture for toric varieties.Final version. 75 pages, 12 figuresSymplectic GeometryAlgebraic GeometryGeometric Topology14J32 (Primary), 53D40, 58E05 (Secondary)text