A general Seifert-van Kampen theorem for algebraic fundamental groups
type: Item
instance of: scholarly article
title: A general Seifert-van Kampen theorem for algebraic fundamental groups
zbMATH Open document ID: 1109.14023
author: Jakob Stix
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2007-02-01T00:00:00Z
review text: A Seifert-Van Kampen theorem describes the fundamental group of a space in terms of the fundamental groups of the constituents of a covering and the configuration of connected components of the covering. Here the author provides the combinatorial part of such a theorem for the most general sort of coverings. Hence a Seifert-Van Kampen theorem is reduced to a purely geometric statement of effective descent. Most of the paper is in the set-up of algebraic fundamental groups of schemes, but the classical case is covered. Examples are in number theory, rigid and formal geometry and in logarithmic geometry.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 5120440
zbMATH Keywords: logarithmic fundamental group
zbMATH Keywords: effective descent
zbMATH Keywords: algebraic fundamental group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1166642159
OpenAlex ID: W1981285457
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DOI: 10.2977/PRIMS/1166642159
description: scientific article; zbMATH DE number 5120440