6

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 $P$?

Martin Brandenburg
  • 181,922
  • This question has remained dormant for so many years, so I am adding this comment, hoping experts on this topic can notice this question. I think $F$ is nothing but the classifying stack $[S/\mathrm{G}_m]$, where $\mathrm{G}_m$ acts on $S$ trivially. So a natural presentation is $S\to [S/\mathrm{G}_m]$. – user393795 Apr 24 '24 at 06:06

0 Answers0