Classification of holomorphic vector bundles on noncommutative two-tori

Abstract

We prove that every holomorphic vector bundle on a noncommutative two-torus $T$ can be obtained by successive extensions from standard holomorphic bundles considered in [2]. This implies 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.