Log Fundamental Group Scheme

TL;DR

This paper extends the concept of the Nori fundamental group scheme to log schemes, providing a classification of torsors in the log flat topology and computing specific quotients with applications to log points.

Contribution

It introduces the log Nori fundamental group scheme and computes its nilpotent pro-p quotient for certain log points, advancing the understanding of fundamental groups in log geometry.

Findings

Defined the log Nori fundamental group scheme.

Computed the nilpotent pro-p quotient with log at {0, 1, ∞}.

Extended classical fundamental group concepts to log schemes.

Abstract

In this article, we study the log-scheme theoretic version of the Nori fundamental group scheme. Similar to the classical Nori fundamental group scheme, the log Nori fundamental group scheme classifies torsors on log flat topology. We also compute the nilpotent pro-p quotient of the log Nori fundamental group scheme with log at $\{0, 1, \infty\}$.