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Semi-finite vector bundles on complex tori

Pavan Adroja, Sanjay Amrutiya

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.

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.
Paper Structure (3 sections, 6 theorems, 32 equations)

This paper contains 3 sections, 6 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Semi--finite bundles on complex torus

Key Result

Lemma 3.1

Let $X=V/\Lambda$ be a complex torus of complex dimension $g$, and let $E$ be a finite holomorphic vector bundle on $X$. Then, where $L_i$'s are torsion line bundles on $X$.

Theorems & Definitions (20)

  • Definition 2.1: No
  • Definition 2.2: No
  • Definition 2.3: Ot
  • Remark 2.4
  • Remark 2.5
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • ...and 10 more