The Stacks project

Definition 38.4.6. Let $S$, $X$, $\mathcal{F}$, $x$, $s$ be as in Definition 38.4.2. Let $(Z, Y, i, \pi , \mathcal{G}, z, y)$ be a one step dévissage of $\mathcal{F}/X/S$ at $x$. Let us define a standard shrinking of this situation to be given by standard opens $S' \subset S$, $X' \subset X$, $Z' \subset Z$, and $Y' \subset Y$ such that $s \in S'$, $x \in X'$, $z \in Z'$, and $y \in Y'$ and such that

\[ (Z', Y', i|_{Z'}, \pi |_{Z'}, \mathcal{G}|_{Z'}, z, y) \]

is a one step dévissage of $\mathcal{F}|_{X'}/X'/S'$ at $x$.

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