The Stacks project

66.2 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 $X \times X$. The reason is that we want to avoid confusion when changing base schemes, as in Spaces, Section 65.16.