Loop group schemes and Abhyankar's lemma

TL;DR

This paper introduces the concept of reductive group schemes over localized regular henselian rings with normal crossing divisors and establishes criteria for the existence of specific parabolic subgroups.

Contribution

It defines reductive group schemes in this context and provides new criteria for the existence of parabolic subgroups of a given type.

Findings

Defined reductive group schemes over localized regular henselian rings.

Provided criteria for the existence of parabolic subgroups.

Extended the theory of group schemes in the context of Abhyankar's lemma.

Abstract

We define the notion of reductive group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor $D$. We provide a criterion for the existence for parabolic subgroups of a given type.