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Linearizaton of group stack actions and the Picard group of the moduli of \(SL_r/\mu_s\)-bundles on a curve. (English) Zbl 0936.14024
Summary: In this paper, we consider morphisms of algebraic stacks \(\mathcal X \to \mathcal Y\) which are torsors under a group stack \(\mathcal G\). We show that line bundles on \(\mathcal Y\) correspond exactly with \(\mathcal G\)-linearized line bundles on \(\mathcal X\) (with a suitable definition of a \(\mathcal G\)-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 \(A_n\).

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