Geodesic
Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks
Documenta mathematica, Tome 25 (2020), pp. 159-169.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. In [\textit{I. Biswas} and \textit{J. P. P. dos Santos}, J. Inst. Math. Jussieu 10, No. 2, 225--234 (2011; Zbl 1214.14037)] and [\textit{M. Antei} and \textit{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 $k$.
Classification : 14A20, 14F08, 14L15, 18F99
Keywords: essentially finite vector bundles, Nori's fundamental group, fundamental gerbes, algebraic stacks 
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     author = {Tonini, Fabio and Zhang, Lei},
     title = {Essentially {Finite} {Vector} {Bundles} on {Normal} {Pseudo-Proper} {Algebraic} {Stacks}},
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Tonini, Fabio; Zhang, Lei. Essentially Finite Vector Bundles on Normal Pseudo-Proper Algebraic Stacks. Documenta mathematica, Tome 25 (2020), pp. 159-169. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a65/