Definition 97.5.1. Let $S$ be a locally Noetherian scheme. Let $\mathcal{Z}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We say $\mathcal{Z}$ satisfies *condition (RS)* if for every pushout

in the category of schemes over $S$ where

$X$, $X'$, $Y$, $Y'$ are spectra of local Artinian rings,

$X$, $X'$, $Y$, $Y'$ are of finite type over $S$, and

$X \to X'$ (and hence $Y \to Y'$) is a closed immersion

the functor of fibre categories

is an equivalence of categories.

## Comments (0)