= Sheaf associated with a graded module
{title2=$\widetilde M|_{D_+(f)}=\widetilde{(M_f)_0}$}
A <graded module> $M$ over a graded ring $S$ determines a <quasi-coherent sheaf> on the <Proj construction> $\operatorname{Proj}S$ by taking the degree-zero part of its localization on each <standard affine open of Proj>. Localization identifies these module sheaves on overlaps. The construction is exact, by <exactness of localization> and exactness of taking a fixed graded component.
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