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Galois Categories

  • Anna CadoretEmail author
Conference paper
Part of the Progress in Mathematics book series (PM, volume 304)

Abstract

These notes describe the formalism of Galois categories and fundamental groups, as introduced by A. Grothendieck in [SGA1, Chap. V]. This formalism stems from Galois theory for topological covers and can be regarded as the natural categorical generalization of it. But, far beyond providing a uniform setting for the preexisting Galois theories as those of topological covers and field extensions, this formalism gave rise to the construction and theory of the étale fundamental group of schemes −one of the major achievements of modern algebraic geometry.

Keywords

Galois categories algebraic geometry étale fundamental group arithmetic geometry 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Centre de Mathématiques Laurent SchwartzEcole PolytechniquePalaiseau cedexFrance

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