On the S-fundamental group scheme

Langer, Adrian

Annales de l'Institut Fourier, Tome 61 (2011) no. 5, pp. 2077-2119.

Nous introduisons un nouveau schéma en groupes fondamental pour les variétés définies sur un corps algébriquement clos (ou simplement parfait) de caractéristique positive. Nous utilisons ce schéma en groupes pour étudier des généralisations en caractéristique positive des résultats de C. Simpson. Nous étudions également quelques propriétés de ce schéma en groupes fondamental, en particulier nous obtenons des résultats de type “Lefschetz”.

We introduce a new fundamental group scheme for varieties defined over an algebraically closed (or just perfect) field of positive characteristic and we use it to study generalization of C. Simpson’s results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.

Classification : 14J60, 14F05, 14F35, 14L15
Keywords: Fundamental group, positive characteristic, numerically flat bundles, Lefschetz type theorems
Mot clés : groupe fondamental, caractéristique positive, fibres numériquement plate, résultats type “Lefschetz”

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