2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132417We establish a, and conjecture further, relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of certain sheaf cohomology. The main ingredient is the Generic Vanishing criterion of math.AG/0608127, based on the Fourier-Mukai transform.12 pages; final version, to appear in Math. Annalen; contains expository changes and a proof in the case of abelian varieties of the generic vanishing criterion we use, according to suggestions from the refereeAlgebraic Geometry14K12; 14F17text