Direct image of a coherent sheaf under a closed immersion
= Direct image of a coherent sheaf under a closed immersion
If $i:Z\hookrightarrow X$ is a <closed immersion> of <Noetherian scheme>[Noetherian schemes] and $\mathcal F$ is a <coherent sheaf> on $Z$, then $i_*\mathcal F$ is coherent on $X$. Affine-locally this regards a finitely generated $A/I$-module as a finitely generated $A$-module.