The Line Bundles on Moduli Stacks of Principal Bundles on a Curve

Let $G$ be an affine reductive algebraic group over an algebraically closed field $k$. We determine the Picard group of the moduli stacks of principal $G$--bundles on any smooth projective curve over $k$.

2010 Mathematics Subject Classification: 14C22, 14D20, 14H10

Keywords and Phrases: principal bundle, moduli stack, Picard group

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