The Stacks project

Situation 99.11.1. Let $S$ be a scheme. Let $f : X \to B$ be a morphism of algebraic spaces over $S$. We define

\[ \mathrm{Pic}_{X/B} : (\mathit{Sch}/B)^{opp} \longrightarrow \textit{Sets} \]

as the fppf sheafification of the functor which to a scheme $T$ over $B$ associates the group $\mathop{\mathrm{Pic}}\nolimits (X_ T)$.

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View Situation 99.11.1 as pdf