Classification of Holomorphic Vector Bundles on Noncommutative Two-Tori

We prove that every holomorphic vector bundle on a noncommutative two-torus T can be obtained by successive exten- sions from standard holomorphic bundles considered in (2). This im- plies that the category of holomorphic bundles on T is equivalent to the heart of a certain t-structure on the derived category of coherent sheaves on an elliptic curve.