Definition 44.4.1 (0B9L)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 44: Picard Schemes of Curves
Section 44.4: The Picard functor
Definition 44.4.1 (cite)

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Definition 44.4.1. Let $\mathit{Sch}_{fppf}$ be a big site as in Topologies, Definition 34.7.8. Let $f : X \to S$ be a morphism of this site. The Picard functor $\mathrm{Pic}_{X/S}$ is the fppf sheafification of the functor

$(\mathit{Sch}/S)_{fppf} \longrightarrow \textit{Sets},\quad T \longmapsto \mathop{\mathrm{Pic}}\nolimits (X_ T)$

If this functor is representable, then we denote $\underline{\mathrm{Pic}}_{X/S}$ a scheme representing it.

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