The Stacks project

78.2 Conventions

The standing assumption is that all schemes are contained in a big fppf site $\mathit{Sch}_{fppf}$. And all rings $A$ considered have the property that $\mathop{\mathrm{Spec}}(A)$ is (isomorphic) to an object of this big site.

Let $S$ be a scheme and let $X$ be an algebraic space over $S$. In this chapter and the following we will write $X \times _ S X$ for the product of $X$ with itself (in the category of algebraic spaces over $S$), instead of $X \times X$.

We continue our convention to label projection maps starting with index $0$, so we have $\text{pr}_0 : X \times _ S Y \to X$ and $\text{pr}_1 : X \times _ S Y \to Y$.