Loop torsors and Abhyankar's lemma

TL;DR

This paper introduces the concept of loop torsors over specific group schemes in algebraic geometry, providing a Galois cohomological classification criterion and revisiting related torsors on Laurent polynomial rings.

Contribution

It defines loop torsors in a new setting and offers a cohomological criterion for their classification, extending existing theories on Laurent polynomial rings.

Findings

Established a classification criterion for loop torsors

Extended the theory to Laurent polynomial rings

Provided new insights into torsors over regular henselian rings

Abstract

We define the notion of loop torsors under certain group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor D. We provide a Galois cohomological criterion for classifying those torsors. We revisit also the related theory of loop torsors on Laurent polynomial rings.