Revêtements étales et groupe fondamental (SGA 1)

论基本群概形的存在性

Sur l'existence du schéma en groupes fondamental

本文研究 Dedekind 概形上连通概形的基本群概形存在性，并引入分类拟有限 torsor 的拟有限基本群概形及 Galois torsor。

Le lemme fondamental pour les groupes unitaires

Let G be an unramified reductive group over a non archimedian local field F. The so-called "Langlands Fundamental Lemma" is a family of conjectural identities between orbital integrals for G(F) and orbital integrals for endoscopic groups of G. In this paper we prove the Langlands fundamental lemma in the particular case where F is a finite extension of F_p((t)), G is a unitary group and p>rank(G). Waldspurger has shown that this particular case implies the Langlands fundamental lemma for unitary groups of rank <p when F is any finite extension of Q_p. We follow in part a strategy initiated by …

Une remarque sur les courbes de Reichardt-Lind et de Schinzel

We prove that the arithmetic fundamental group of X admits no section over the absolute Galois group of Q when X is the Schinzel curve, thereby confirming in this example the prediction given by Grothendieck's section conjecture. ----- Nous démontrons que le groupe fondamental arithmétique de X n'admet pas de section au-dessus du groupe de Galois absolu de Q lorsque X est la courbe de Schinzel, confirmant ainsi sur cet exemple la prédiction donnée par la conjecture des sections de Grothendieck.

Groupes Classiques

We introduce so-called "classical" algebraic group over a general base scheme, and then place them where they belong in the classification of reductive groups established in SGA3. We cover the non-split cases and we describe on the way several categories of torsors.