Linearization of group stack actions and the Picard group of the moduli of \SL_r/\mu_s-bundles on a curve

Abstract

We first study the descent theory of line bundles under a morphism which is tors or under a group stack and then use this technical result to determine the exact structure of \Pic(\M_G) where G=\SL_r/\mu_s (we include a minor modification to explain the genus 0 case).Comment: 13 pages, PlainTe