Let G be a connected reductive group
over an algebraically closed field k, and let
C be a smooth projective curve over k. I'll
describe the Picard group of the moduli stack
of principal G-bundles on C and explain
consequences for the existence of Poincare
families on the corresponding coarse moduli
scheme, and for the Picard group of the latter.
This is joint work with I. Biswas (TIFR, Mumbai).