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

## TL;DR

This paper extends the characterization of essentially finite vector bundles from varieties to normal, connected, strongly pseudo-proper algebraic stacks over arbitrary fields, using a new approach.

## Contribution

It introduces a novel method to analyze essentially finite vector bundles on algebraic stacks, broadening the scope beyond classical varieties.

## Key findings

- Characterization of essentially finite vector bundles on algebraic stacks
- Extension of known results from varieties to stacks
- New approach applicable over arbitrary fields

## Abstract

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. It is known that a vector bundle $V$ on $X$ is essentially finite if and only if it is trivialized by a proper surjective morphism $f:Y\to X$. 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 $k$.