Semi-finite vector bundles on complex tori

Abstract

We study finite and semi-finite vector bundles on complex tori. We give an explicit decomposition of such bundles in terms of torsion and unipotent factors. As a consequence, we prove that the extended Nori fundamental group scheme of a complex torus decomposes as the product of its etale fundamental group scheme and its unipotent fundamental group scheme.

arXiv comment8 pages. Accepted for publication in the Journal of Mathematical Sciences, the University of Tokyo