The Stacks project

Definition 17.29.8. Let $(f, f^\sharp ) : (X, \mathcal{O}_ X) \to (S, \mathcal{O}_ S)$ be a morphism of ringed spaces. Let $\mathcal{F}$ and $\mathcal{G}$ be $\mathcal{O}_ X$-modules. Let $k \geq 0$ be an integer. A differential operator of order $k$ on $X/S$ is a differential operator $D : \mathcal{F} \to \mathcal{G}$ with respect to $f^\sharp : f^{-1}\mathcal{O}_ S \to \mathcal{O}_ X$ We denote $\text{Diff}^ k_{X/S}(\mathcal{F}, \mathcal{G})$ the set of these differential operators.