Vector bundles trivialized by proper morphisms and the fundamental group scheme

Biswas, Indranil ; dos Santos, Joao Pedro P. (2010) Vector bundles trivialized by proper morphisms and the fundamental group scheme Journal of the Institute of Mathematics of Jussieu . ISSN 1474-7480

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Related URL: http://dx.doi.org/10.1017/S1474748010000071

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.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:Essentially Finite Vector Bundle; Fundamental Group Scheme; Trivialization
ID Code:3498
Deposited On:12 Oct 2010 04:24
Last Modified:16 May 2016 14:17

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