Algebraization of bundles on non-proper schemes

TL;DR

This paper investigates the conditions under which principal bundles with reductive structure groups can be algebraized on non-proper schemes, establishing existence results for codimension at least 3 and precise criteria for codimension 2.

Contribution

It provides new algebraization criteria for principal bundles on non-proper schemes, extending previous results to cases with codimension 2 and higher.

Findings

Algebraization always exists when the closed subset has codimension at least 3.

For codimension 2, algebraization exists if and only if a specific condition is met.

The paper clarifies the algebraization problem in the context of non-proper schemes.

Abstract

We consider the algebraization problem for principal bundles with reductive structure group, defined on the complement of a closed subset Z in a proper formal scheme. We show that, when Z is of codimension at least 3, an algebraization always exists. For codimension 2 we show that an algebraization exists precisely when a certain additional condition is satisfied.