Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks

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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\longrightarrow 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 .