Unipotent Schottky bundles on Riemann surfaces and complex tori

Abstract

We study a natural map from representations of a free (resp. free abelian) group of rank g in GL_r(C), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (resp. complex torus X of dimension g). This map defines what is called a Schottky functor. Our main result is that this functor induces an equivalence between the category of unipotent representations of Schottky groups and the category of unipotent vector bundles on X. We also show that, over a complex torus, any vector or principal bundle with a flat holomorphic connection is Schottky.

In v3, the results are approached using standard cohomology and derived functor arguments, avoiding extensive use of Yoneda Extensions

References in corpus (1)

• Schottky uniformization and vector bundles over Riemann surfaces

Cited by in corpus (1)

• Principal Schottky Bundles over Riemann surfaces