About: Algebraic space

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In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the étale topology.

Attributes	Values
rdfs:label	Algebraic space (en)
rdfs:comment	In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the étale topology. (en)
dcterms:subject	Algebraic geometry
Wikipage page ID	2394027 (xsd:integer)
Wikipage revision ID	1046298299 (xsd:integer)
Link from a Wikipage to another Wikipage	Deformation theory Algebraic function Indeterminate (variable) Affine scheme Quasi-separated Analytic space Mathematics Quotient stack Equivalence class Hopf manifold Stack (mathematics) Local ring Algebraic geometry Equivalence relation Oxford University Press Hironaka's example Keel–Mori theorem Free action Ring (mathematics) Covering space Algebraic geometry Codimension Moduli space Michael Artin Category (mathematics) Scheme (mathematics) Étale morphism Étale topology Zariski topology Finite group Moishezon manifold Springer-Verlag Grothendieck Descent (category theory)
Link from a Wikipage to an external page	https://books.google.com/books/%3Fid=3evuAAAAMAAJ https://books.google.com/books/about/Algebraic_spaces.html%3Fid=Gl7vAAAAMAAJ http://stacks.math.columbia.edu/tag/025R
sameAs	Algebraic space Algebraic space Algebraic space
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Citation dbt:Reflist dbt:Sfnm
1a	Artin (en)
1y	1969 (xsd:integer)
2a	Artin (en)
2y	1971 (xsd:integer)
first	V.I. (en)
id	a/a011630 (en)
last	Danilov (en)
title	Algebraic space (en)
has abstract	In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the étale topology. The resulting category of algebraic spaces extends the category of schemes and allows one to carry out several natural constructions that are used in the construction of moduli spaces but are not always possible in the smaller category of schemes, such as taking the quotient of a free action by a finite group (cf. the Keel–Mori theorem). (en)
prov:wasDerivedFrom	wikipedia-en:Algebraic_space?oldid=1046298299&ns=0
page length (characters) of wiki page	11000 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Algebraic_space
is Link from a Wikipage to another Wikipage of	Algebraic stack Derivator Prestack Timeline of category theory and related mathematics Quotient stack Quasi-separated morphism Glossary of algebraic geometry Chow group Deligne–Mumford stack Space (mathematics) Stack (mathematics) K-stability of Fano varieties Algebraic geometry Algebraic variety Ample line bundle Gerbe Hironaka's example Keel–Mori theorem Hilbert scheme Cotangent complex Torsor (algebraic geometry) Weil restriction Moduli scheme Moduli space Artin's criterion Michael Artin Scheme (mathematics) Moishezon manifold Glossary of algebraic geometry Éléments de géométrie algébrique Étale equivalence relation
is Wikipage redirect of	Étale equivalence relation
is foaf:primaryTopic of	wikipedia-en:Algebraic_space

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