The Jordan property for local fundamental groups

TL;DR

This paper proves the Jordan property for local fundamental groups of klt singularities and establishes effective index one covers, advancing understanding of their structure and local class groups.

Contribution

It introduces the Jordan property for regional fundamental groups of klt singularities and constructs effective simultaneous index one covers, providing new tools for their analysis.

Findings

Proves Jordan property for regional fundamental groups of klt singularities.

Establishes existence of effective simultaneous index one covers.

Applies results to local class groups of klt singularities.

Abstract

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index one covers for $n$-dimensional klt singularities. We give an application to the study of local class groups of klt singularities.