Volume 26, issue 1 (2022)

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The Jordan property for local fundamental groups

Lukas Braun, Stefano Filipazzi, Joaquín Moraga and Roberto Svaldi

Geometry & Topology 26 (2022) 283–319
DOI: 10.2140/gt.2022.26.283

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n–dimensional klt singularities. We give an application to the study of local class groups of klt singularities.

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Local fundamental group, klt singularities, Jordan property
Mathematical Subject Classification
Primary: 14B05, 14E20, 14F35
Secondary: 14E30
Received: 24 June 2020
Revised: 30 December 2020
Accepted: 9 February 2021
Published: 5 April 2022
Proposed: Dan Abramovich
Seconded: Mark Gross, Richard P Thomas
Lukas Braun
Mathematisches Institut
Albert-Ludwigs-Universität Freiburg
Freiburg im Breisgau
Stefano Filipazzi
Institute of Mathematics
Joaquín Moraga
Department of Mathematics
Princeton University
Princeton, NJ
United States
Roberto Svaldi
Institute of Mathematics