Picard groups for line bundles with connection

TL;DR

This paper explores the structure of Picard groups when considering line bundles equipped with connections on smooth analytic or algebraic varieties, providing a unified approach for both contexts.

Contribution

It introduces a novel framework for Picard groups of line bundles with connections applicable to both analytic and algebraic varieties.

Findings

Develops a unified approach for Picard groups with connections

Extends classical Picard group concepts to include connections

Provides foundational results for line bundles with connections

Abstract

We study analogues of the usual Picard group for smooth analytic or non-singular algebraic varieties but instead of line bundles we study line bundles with a connection. We choose an approach which works for both cases.