  In this paper we study the holomorphic bundles over a noncommutative complex
torus. We define a noncommutative abelian variety as a kind of deformation of
abelian variety and we show that for a restricted deformation parameter, one
can define a noncommutative abelian variety. Also, along the cohomological
deformation, we discuss the noncommutative analogue of usual Riemann
conditions. This will be done by using the real cohomologies instead of the
rational ones.
