Definition 38.4.2. Let S be a scheme. Let X be locally of finite type over S. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module of finite type. Let x \in X be a point with image s in S. A one step dévissage of \mathcal{F}/X/S at x is a system (Z, Y, i, \pi , \mathcal{G}, z, y), where (Z, Y, i, \pi , \mathcal{G}) is a one step dévissage of \mathcal{F}/X/S over s and
\dim _ x(\text{Supp}(\mathcal{F}_ s)) = \dim (\text{Supp}(\mathcal{F}_ s)),
z \in Z is a point with i(z) = x and \pi (z) = y,
we have \pi ^{-1}(\{ y\} ) = \{ z\} ,
the extension \kappa (y)/\kappa (s) is purely transcendental.
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