2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68312We prove that every holomorphic vector bundle on a noncommutative two-torus $T$ can be obtained by successive extensions from standard holomorphic bundles considered in math.QA/0211262. This implies that the category of holomorphic bundles on $T$ is equivalent to the heart of certain $t$-structure on the derived category of coherent sheaves on an elliptic curve.AMSLatex, 18 pagesQuantum AlgebraAlgebraic Geometrytext