International audienceWe study stratified sheaves in positive characteristic algebraic geometry using the technique of Tannakian categories. We show that the associated Tannakian group scheme Π is a perfect scheme. We also prove that in the proper case the largest unipotent quotient of Π is pro-etale. Special attention is paid to abelian varieties, where a description of Π is obtained. We finish with a discussion of the case where the ground field is value

No abstract

Let X be a smooth projective variety defined over an algebraically closed field k. Nori constructed a category of vector bundles on X, called essentially finite vector bundles, which is reminiscent of the category of representations of the fundamental group (in characteristic zero). In fact, this category is equivalent to the category of representations of a pro-finite group scheme which controls all finite torsors. We show that essentially finite vector bundles coincide with those which become trivial after being pulled back by some proper and surjective morphism to X.