Loop torsors. Theory and applications

TL;DR

This paper develops a comprehensive theory of loop torsors over Laurent polynomial rings, extending their applicability to positive characteristic and non-finite type group schemes, and explores the relationship with toral torsors.

Contribution

It provides a complete analysis of the relation between loop and toral torsors in a broad setting, advancing the understanding of torsors in algebraic geometry.

Findings

Established the equivalence of loop and toral torsors in general cases

Extended the theory of loop torsors to positive characteristic

Applied the theory to non-finite type group schemes

Abstract

Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theory that can yields results in positive characteristic, and for group schemes that are not of finite type. The relation between loop and so-called toral torsors, is one of the central questions in the area. The present paper addresses this question in full generality.