----- > [!proposition] Proposition. ([[quasicoherence pushes forward]]) > If $f:X\to Y$ is a [[morphism of locally ringed spaces|scheme morphism]] and $\mathcal{F}$ is a [[quasicoherent sheaf|quasicoherent]] [[sheaf]] of $\mathcal{O}_{X}$-[[sheaf of modules|modules]] on $X$, then $f_{*}\mathcal{F}$ is a [[quasicoherent sheaf|quasicoherent]] [[sheaf]] of $\mathcal{O}_{Y}$-[[module|modules]] on $Y$. ^proposition > [!proof]- Proof. ([[quasicoherence pushes forward]]) > ~ ----- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```