Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks

Abstract

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. In [I. Biswas and J. P. P. dos Santos, J. Inst. Math. Jussieu 10, No. 2, 225–234 (2011; Zbl 1214.14037)] and [M. Antei and V. B. Mehta, Arch. Math. 97, No. 6, 523–527 (2011; Zbl 1236.14041)] it is proved that a vector bundle $V$ on $X$ is essentially finite if and only if it is trivialized by a proper surjective morphism $f:Y⟶X$. In this paper we introduce a different approach to this problem which allows to extend the results to normal, connected and strongly pseudo-proper algebraic stack of finite type over an arbitrary field $k$.