Vector bundles trivialized by proper morphisms and the fundamental group scheme, II

Details Vector bundles trivialized by proper morphisms and the fundamental group scheme, II Vector bundles trivialized by proper morphisms and the fundamental group scheme, II

2010-04-21

arxiv.org/abs/1004.3609v3

Mathematics

Algebraic Geometry

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Scientific paper

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 etale group scheme. We give a counterexample to this conclusion in the absence of separability.

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