Reduced induced subscheme
= Reduced induced subscheme
{wiki=Reduced_scheme#Reduced_subscheme}
Every closed subset $Z\subseteq X$ has a canonical reduced closed-subscheme structure defined affine-locally by $\operatorname{Spec}(A/\sqrt I)$ when $Z=V(I)\subseteq\operatorname{Spec}A$. It is the smallest closed subscheme with underlying set $Z$.