Mathematics – Algebraic Geometry
Scientific paper
2009-12-18
Mathematics
Algebraic Geometry
Final version
Scientific paper
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.
Biswas Indranil
dos Santos Joao Pedro P.
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