# Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks

### Fabio Tonini

Dipartimento di Matematica e Informatica ``Ulisse Dini'', Universitá degli Studi di Firenze, Viale Morgagni, 67/a, Florence 50134, Italy### Lei Zhang

Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

## 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 $f:Y\longrightarrow X$. 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 $k$.

## Cite this article

Fabio Tonini, Lei Zhang, Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks. Doc. Math. 25 (2020), pp. 159–169

DOI 10.4171/DM/742