Restriction of a module sheaf to a closed subvariety
= Restriction of a module sheaf to a closed subvariety
{title2=$\widetilde M|_{\operatorname{Spec}(A/I)}=\widetilde{M/IM}$}
The restriction meant here is the <pullback of a sheaf of modules> to the closed subvariety, including tensoring with its structure sheaf. On an <affine chart>, tensoring $M$ with $A/I$ gives $M/IM$. This distinction matters because restricting only the underlying topological sheaf would retain the ambient ring action.