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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
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 1 covers for n–dimensional klt singularities. We give an application to the study of local class groups of klt singularities.

Keywords
Local fundamental group, klt singularities, Jordan property
Mathematical Subject Classification
Primary: 14B05, 14E20, 14F35
Secondary: 14E30
References
Publication
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
Authors
Lukas Braun
Mathematisches Institut
Albert-Ludwigs-Universität Freiburg
Freiburg im Breisgau
Germany
http://home.mathematik.uni-freiburg.de/braun/
Stefano Filipazzi
Institute of Mathematics
EPFL
Lausanne
Switzerland
https://sma.epfl.ch/~filipazz/
Joaquín Moraga
Department of Mathematics
Princeton University
Princeton, NJ
United States
https://web.math.princeton.edu/~jmoraga/
Roberto Svaldi
Institute of Mathematics
EPFL
Lausanne
Switzerland
http://sma.epfl.ch/~svaldi/