Vector Bundles over Normal Varieties Trivialized by Finite Morphisms

TL;DR

The paper proves that vector bundles over normal projective varieties that become trivial after a finite surjective morphism are essentially finite, linking trivialization by finite covers to a finiteness property.

Contribution

It establishes that trivialization of vector bundles by finite morphisms implies their essential finiteness over normal projective varieties.

Findings

Vector bundles trivialized by finite morphisms are essentially finite.

Finite surjective morphisms trivialize certain vector bundles.

The result applies to normal, projective varieties over algebraically closed fields.

Abstract

Let $Y$ be a normal and projective variety over an algebraically closed field $k$ and $V$ a vector bundle over $Y$. We prove that if there exist a $k$-scheme $X$ and a finite surjective morphism $g:X\to Y$ that trivializes $V$ then $V$ is essentially finite.