A general Seifert-van Kampen theorem for algebraic fundamental groups
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.
scientific article; zbMATH DE number 5120440
scientific article