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The cohomology groups of line bundles over complex tori (or abelianvarieties) are classically studied invariants of these spaces. In this article,we compute the cohomology groups of line bundles over various holomorphic,non-commutative deformations of complex tori. Our analysis interpolates betweentwo extreme cases. The first case is a calculation of the space of(cohomological) theta functions for line bundles over constant, commutativedeformations. The second case is a calculation of the cohomologies ofnon-commutative deformations of degree-zero line bundles.

Cohomology Groups of Deformations of Line Bundles on Complex Tori