Proposition 58.27.1. Let k be a field. Let X be a proper scheme over k. Let \mathcal{L} be an ample invertible \mathcal{O}_ X-module. Let s \in \Gamma (X, \mathcal{L}). Let Y = Z(s) be the zero scheme of s. Assume that for all x \in X \setminus Y we have
Then the restriction functor \textit{FÉt}_ X \to \textit{FÉt}_ Y is fully faithful. In fact, for any open subscheme V \subset X containing Y the restriction functor \textit{FÉt}_ V \to \textit{FÉt}_ Y is fully faithful.
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