Example of a Picard stack

301 Views Asked by At

Let $F$ be the stack (over some base scheme $S$) which associates to every scheme $X$ the groupoid of invertible sheaves on $X$. Then by the general theory (see for example Aoki's paper) $F$ is algebraic. My question is: Can you write down a nice presentation $P \to F$ explicitly, i.e. a surjective smooth morphism from a scheme $P$?