Bundles on non-proper schemes: representability

TL;DR

This paper proves that the functor of principal G-bundles on a proper scheme satisfying Serre's condition S2, defined away from a codimension at least 3 subset, is representable as an algebraic stack.

Contribution

It establishes the algebraic stack structure for principal G-bundles on non-proper schemes under specific conditions, extending previous representability results.

Findings

The functor of principal G-bundles is an algebraic stack.

Representation holds for schemes satisfying Serre's S2 condition.

Applicability to bundles defined away from high codimension subsets.

Abstract

Let X be a proper scheme over a field k which satisfies Serre's condition S2 and G a reductive group over k. We prove that the functor of principal G-bundles defined away from a non-fixed closed subset in X of codimension at least 3, is an algebraic stack in the sense of Artin.