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Zbl 0936.14024
Laszlo, Yves
Linearizaton of group stack actions and the Picard group of the moduli of $SL_r/\mu_s$-bundles on a curve. (English)
[J] Bull. Soc. Math. Fr. 125, No.4, 529-545 (1997). ISSN 0037-9484

Summary: In this paper, we consider morphisms of algebraic stacks $\Cal X \to \Cal Y$ which are torsors under a group stack $\Cal G$. We show that line bundles on $\Cal Y$ correspond exactly with $\Cal G$-linearized line bundles on $\Cal X$ (with a suitable definition of a $\Cal G$-linearization). We use this fact to determine the precise structure of the Picard group of the moduli stack of $G$-bundles on an algebraic curve when $G$ is any group of type $A_n$.
[Xiaotao Sun (Beijing)]

MSC 2000:: *14H60 Vector bundles on curves
14C22 Picard groups
14H10 Families, algebraic moduli (curves)
14L30 Group actions on varieties or schemes

Keywords: linearization; morphisms of algebraic stacks; Picard group; torsors; moduli stack on an algebraic curve

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