About: Étale morphism

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In algebraic geometry, an étale morphism (French: [etal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology.

Attributes	Values
rdfs:label	Morfismo étale (it) 에탈 사상 (ko) エタール射 (ja) Étale morphism (en)
rdfs:comment	In geometria algebrica, un morfismo étale (dal francese: calmo, immobile, qualcosa lasciato a stabilirsi.) è un morfismo di schemi che è ed è . Un morfismo étale è l'analogo algebrico della nozione di isomorfismo locale nella topologia euclidea. I morfismi étale soddisfano le ipotesi del teorema della funzione implicita, ma poiché gli aperti nella topologia di Zariski sono grandi, tali morfismi non sono necessariamente isomorfismi locali. Nonostante ciò, i morfismi étale conservano molte delle proprietà degli isomorfismi analitici locali e sono utili per definire il e la . (it) エタール射（エタールしゃ、étale morphism）とは、数学において間の平坦かつ不分岐な射のこと。「étale」という形容詞は複素解析幾何学（géométrie analytique complexe）における古典的な概念「domaine étalé」から採られた。 (ja) In algebraic geometry, an étale morphism (French: [etal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology. (en)
dcterms:subject	Morphisms of schemes
Wikipage page ID	3022771 (xsd:integer)
Wikipage revision ID	1084286242 (xsd:integer)
Link from a Wikipage to another Wikipage	Monic polynomial Ringed space Quasi-finite morphism Radicial morphism Galois theory Branched covering Submersion (mathematics) Morphisms of schemes Tangent space Publications Mathématiques de l'IHÉS Adjective Algebraic Geometry (book) Algebraic geometry Flat morphism Formally étale morphism Parabola Formal derivative Quasi-compact morphism Purity (algebraic geometry) Regular map (algebraic geometry) Jacobian matrix and determinant Jean Dieudonné Diffeomorphisms Manifold Square root Grothendieck's Galois theory Glossary of scheme theory Implicit function theorem Separable closure Scheme (mathematics) Étale topology Unramified morphism Completion (ring theory) Formally étale Zariski topology Smooth morphism Ring homomorphism Springer-Verlag Open subset Algebraic fundamental group
Link from a Wikipage to an external page	https://archive.org/details/etalecohomology00miln http://www.jmilne.org/math/CourseNotes/LEC.pdf
sameAs	Étale morphism Étale morphism Étale morphism Étale morphism Étale morphism Étale morphism
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:IPA-fr dbt:Reflist
has abstract	In geometria algebrica, un morfismo étale (dal francese: calmo, immobile, qualcosa lasciato a stabilirsi.) è un morfismo di schemi che è ed è . Un morfismo étale è l'analogo algebrico della nozione di isomorfismo locale nella topologia euclidea. I morfismi étale soddisfano le ipotesi del teorema della funzione implicita, ma poiché gli aperti nella topologia di Zariski sono grandi, tali morfismi non sono necessariamente isomorfismi locali. Nonostante ciò, i morfismi étale conservano molte delle proprietà degli isomorfismi analitici locali e sono utili per definire il e la . (it) In algebraic geometry, an étale morphism (French: [etal]) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology. The word étale is a French adjective, which means "slack", as in "slack tide", or, figuratively, calm, immobile, something left to settle. (en) エタール射（エタールしゃ、étale morphism）とは、数学において間の平坦かつ不分岐な射のこと。「étale」という形容詞は複素解析幾何学（géométrie analytique complexe）における古典的な概念「domaine étalé」から採られた。 (ja)
gold:hypernym	Morphism
prov:wasDerivedFrom	wikipedia-en:Étale_morphism?oldid=1084286242&ns=0
page length (characters) of wiki page	15529 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Étale_morphism
is Link from a Wikipage to another Wikipage of	Puiseux series Algebraic space Glossary of algebraic geometry Glossary of commutative algebra Branched covering Morphism of algebraic varieties Profinite integer Local criterion for flatness Deligne–Mumford stack Étale algebra Étale cohomology Fundamental group Stack (mathematics) Etale covering Etale map Etale morphism Local homeomorphism Nisnevich topology Ernst Witt Flat morphism Formally étale morphism Diffeomorphism Dimension of a scheme Purity (algebraic geometry) Hilbert's Nullstellensatz Cotangent complex Hypercovering Torsor (algebraic geometry) Abhyankar's conjecture Topos Regular scheme

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