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- Quasi-compact_morphism abstract "In algebraic geometry, a morphism between schemes is said to be quasi-compact if Y can be covered by open affine subschemes such that the pre-images are quasi-compact (as topological space). If f is quasi-compact, then the pre-image of a quasi-compact open subscheme (e.g., open affine subscheme) under f is quasi-compact.It is not enough that Y admits a covering by quasi-compact open subschemes whose pre-images are quasi-compact. To give an example, let A be a ring that does not satisfy the ascending chain conditions on radical ideals, and put . X contains an open subset U that is not quasi-compact. Let Y be the scheme obtained by gluing two X's along U. X, Y are both quasi-compact. If is the inclusion of one of the copies of X, then the pre-image of the other X, open affine in Y, is U, not quasi-compact. Hence, f is not quasi-compact.A morphism from a quasi-compact scheme to an affine scheme is quasi-compact.Let be a quasi-compact morphism between schemes. Then is closed if and only if it is stable under specialization.The composition of quasi-compact morphisms is quasi-compact. The base change of a quasi-compact morphism is quasi-compact.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.[citation needed]".
- Quasi-compact_morphism wikiPageExternalLink when-is-an-irreducible-scheme-quasi-compact.
- Quasi-compact_morphism wikiPageID "12410777".
- Quasi-compact_morphism wikiPageRevisionID "508204996".
- Quasi-compact_morphism archive "math.AG".
- Quasi-compact_morphism hasPhotoCollection Quasi-compact_morphism.
- Quasi-compact_morphism id "412512".
- Quasi-compact_morphism subject Category:Morphisms_of_schemes.
- Quasi-compact_morphism comment "In algebraic geometry, a morphism between schemes is said to be quasi-compact if Y can be covered by open affine subschemes such that the pre-images are quasi-compact (as topological space). If f is quasi-compact, then the pre-image of a quasi-compact open subscheme (e.g., open affine subscheme) under f is quasi-compact.It is not enough that Y admits a covering by quasi-compact open subschemes whose pre-images are quasi-compact.".
- Quasi-compact_morphism label "Quasi-compact morphism".
- Quasi-compact_morphism sameAs m.0knw0kn.
- Quasi-compact_morphism sameAs Q7269441.
- Quasi-compact_morphism sameAs Q7269441.
- Quasi-compact_morphism wasDerivedFrom Quasi-compact_morphism?oldid=508204996.
- Quasi-compact_morphism isPrimaryTopicOf Quasi-compact_morphism.