Logarithmic purity and logarithmic Nori fundamental group

TL;DR

This paper extends the logarithmic purity theorem to certain torsors in the Kummer log flat topology and introduces the logarithmic Nori fundamental group, comparing it with classical and tame fundamental groups.

Contribution

It generalizes the logarithmic purity theorem to new torsors and constructs the logarithmic Nori fundamental group for log schemes, linking it to existing fundamental groups.

Findings

Extended purity theorem to Kummer log flat torsors.

Constructed the logarithmic Nori fundamental group.

Compared it with classical and tame fundamental groups.

Abstract

We generalize the logarithmic purity theorem of Fujiwara-Kato to torsors which arise in the Kummer log flat topology under finite flat linearly reductive group schemes. As an application, we construct the logarithmic Nori fundamental group of a log regular log scheme classifying those torsors, and compare it to classical Nori fundamental group and tame fundamental group.