This is a new and updated edition of the first volume of the famous notes from the Séminaire de Géométrie Algébrique (also known as SGA 1) held at the Institute Hautes Études Scientifiques during the 1950s and 1960s. Written mainly by Alexander Grothendieck, with two articles by Michèle Raynaud, the book gives the original presentation of the foundations of fundamental group theory in algebraic geometry, which allows one to treat equally the cases of an algebraic variety in the usual sense and that of the ring of integers in a number field. This volume is suitable for graduate students and research mathematicians interested in algebraic geometry.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

• Morphismes étales
• Morphismes lisses: généralités, propriétés différentielles
• Morphismes lisses: propriétés de prolongement
• Morphismes plats
• Le groupe fondamental: généralités
• Catégories fibrées et descente
• n'existe pas
• Descente fidèlement plate
• Descente des morphismes étales. Application au groupe fondamental
• Théorie de la spécialisation du groupe fondamental
• Exemples et compléments
• Géométrie algébrique et géométrie analytique
• Propreté cohomologique des faisceaux d'ensembles et des faisceaux de groupes non commutatifs
• Index terminologique
• Index des notations