Talk:Quasi-compact morphism

Quasi-compact schemes vs. quasi-compact morphisms

This topic is in need of attention from an expert on the subject.

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The last to paragraphs

An affine scheme is quasi-compact. In fact, a scheme is quasi-compact if and only if it is a finite union of open affine subschemes. Serre’s criterion gives a necessary and sufficient condition for a quasi-compact scheme to be affine.
A quasi-compact scheme has at least one closed point.

relate not to morphisms but to schemes. They either might be better placed in a new article "quasi-compact schemes" or as part of Compact_space#Open_cover_definition. It's not clear to me, which is better. Thus an expert should decide how to resolve this. Tpreu (talk) 10:24, 15 August 2023 (UTC)[reply]

A scheme is quasi-compact iff the unique map to Spec(Z) is a quasi-compact morphism; the article should elaborate that. 1234qwer 1234qwer 4 04:54, 9 January 2025 (UTC)[reply]