I was wondering it while studying Hartshorne.
In II.4.8 proof of the corollary (This part is about valuative criterion of properness.), it is written that a morphism from noetherian scheme is automatically quasi-compact.
Precisely, for a noetherian scheme $X$, any morphism $f:X\rightarrow Y$ of schemes is quasi-compact.
But I cannot find why.
Could you give me any idea?