About: Sheaf of algebras

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Sheaf of algebras Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FSheaf_of_algebras

In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of -modules. It is quasi-coherent if it is so as a module. When X is a scheme, just like a ring, one can take the global Spec of a quasi-coherent sheaf of algebras: this results in the contravariant functor from the category of quasi-coherent (sheaves of) -algebras on X to the category of schemes that are affine over X (defined below). Moreover, it is an equivalence: the quasi-inverse is given by sending an affine morphism to

Attributes	Values
rdfs:label	Sheaf of algebras (en)
rdfs:comment	In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of -modules. It is quasi-coherent if it is so as a module. When X is a scheme, just like a ring, one can take the global Spec of a quasi-coherent sheaf of algebras: this results in the contravariant functor from the category of quasi-coherent (sheaves of) -algebras on X to the category of schemes that are affine over X (defined below). Moreover, it is an equivalence: the quasi-inverse is given by sending an affine morphism to (en)
dcterms:subject	Morphisms of schemes Sheaf theory
Wikipage page ID	56371096 (xsd:integer)
Wikipage revision ID	952868589 (xsd:integer)
Link from a Wikipage to another Wikipage	Quasi-coherent sheaf Morphism of schemes Ringed space Quasi-affine morphism Cone (algebraic geometry) Morphisms of schemes Sheaf of modules Quasi-compact morphism Sheaf theory Serre's theorem on affineness Scheme (mathematics) Separated morphism Finite morphism Locally ringed space Global Spec Sheaf of commutative rings
Link from a Wikipage to an external page	https://ncatlab.org/nlab/show/affine+morphism
sameAs	Sheaf of algebras Sheaf of algebras
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:EGA dbt:Hartshorne_AG
has abstract	In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of -modules. It is quasi-coherent if it is so as a module. When X is a scheme, just like a ring, one can take the global Spec of a quasi-coherent sheaf of algebras: this results in the contravariant functor from the category of quasi-coherent (sheaves of) -algebras on X to the category of schemes that are affine over X (defined below). Moreover, it is an equivalence: the quasi-inverse is given by sending an affine morphism to (en)
prov:wasDerivedFrom	wikipedia-en:Sheaf_of_algebras?oldid=952868589&ns=0
page length (characters) of wiki page	4895 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sheaf_of_algebras
is Link from a Wikipage to another Wikipage of	Integral element Affine morphism Cone (algebraic geometry) Spectrum of a ring Stack (mathematics) Sheaf of modules Associative algebra Proj construction
is Wikipage redirect of	Affine morphism
is foaf:primaryTopic of	wikipedia-en:Sheaf_of_algebras

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software