Rev\^etements \'etales et groupe fondamental (SGA 1)

TL;DR

This paper develops a foundational theory of the fundamental group in Algebraic Geometry, unifying the treatment of algebraic varieties and rings of integers in number fields from a Kronecker perspective.

Contribution

It introduces a unified approach to the fundamental group applicable to both algebraic varieties and rings of integers, bridging geometric and arithmetic contexts.

Findings

Establishes a common framework for fundamental groups in algebraic and arithmetic settings.

Provides foundational results linking geometric and number-theoretic structures.

Lays groundwork for further exploration of fundamental groups in arithmetic geometry.

Abstract

Le texte pr\'esente les fondements d'une th\'eorie du groupe fondamental en G\'eom\'etrie Alg\'ebrique, dans le point de vue ``kroneckerien'' permettant de traiter sur le m\^eme pied le cas d'une vari\'et\'e alg\'ebrique au sens habituel, et celui d'un anneau des entiers d'un corps de nombres, par exemple. The text presents the foundations of a theory of the fundamental group in Algebraic Geometry from the Kronecker point of view, allowing one to treat on an equal footing the case of an algebraic variety in the usual sense, and that of the ring of integers in a number field, for instance.