Semi-finite vector bundles on complex tori

TL;DR

This paper investigates semi-finite vector bundles on complex tori, providing explicit decompositions and revealing the structure of the extended Nori fundamental group scheme as a product of its components.

Contribution

It offers a detailed decomposition of semi-finite vector bundles and describes the fundamental group scheme structure for complex tori.

Findings

Explicit decomposition of semi-finite vector bundles into torsion and unipotent parts

The extended Nori fundamental group scheme decomposes as a product of etale and unipotent schemes

Provides structural insights into 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.