Abstract
Let X be a projective and smooth variety over an algebraically closed field k. Let \(f\, :\ Y \rightarrow X\) be a proper and surjective morphism of k–varieties. Assuming that f is separable, we prove that the Tannakian category associated to the vector bundles E on X such that f ∗ E is trivial is equivalent to the category of representations of a finite and étale group scheme. We give a counterexample to this conclusion in the absence of separability.
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Biswas, I., Santos, J.P.P.d. (2012). Vector Bundles Trivialized by Proper Morphisms and the Fundamental Group Scheme, II. In: Stix, J. (eds) The Arithmetic of Fundamental Groups. Contributions in Mathematical and Computational Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23905-2_3
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DOI: https://doi.org/10.1007/978-3-642-23905-2_3
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