Definition 76.3.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. We say $f$ is radicial if for any morphism $\mathop{\mathrm{Spec}}(K) \to Y$ where $K$ is a field the reduction $(\mathop{\mathrm{Spec}}(K) \times _ Y X)_{red}$ is either empty or representable by the spectrum of a purely inseparable field extension of $K$.
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