About: Formal scheme

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In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes. Formal schemes were motivated by and generalize Zariski's theory of formal holomorphic functions.

Attributes	Values
rdfs:label	Formales Schema (de) Formal scheme (en) 형식적 스킴 (ko)
rdfs:comment	In der algebraischen Geometrie ist ein formales Schema eine Verallgemeinerung eines Schemas. Grob gesagt beschreibt ein formales Schema eine infinitesimale Umgebung eines Schemas. Formale Schemata finden Anwendung in der und . Es gibt verschiedene Definitionen in der Literatur, häufig werden aus technischen Gründen lediglich lokal noethersche formale Schemata definiert. (de) 대수기하학에서 형식적 스킴(形式的scheme, 영어: formal scheme)은 스스로의 ‘무한소 근방’의 데이터를 기억하는, 스킴의 개념의 일반화이다.:190–200, §Ⅱ.9 (ko) In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes. Formal schemes were motivated by and generalize Zariski's theory of formal holomorphic functions. (en)
dct:subject	Algebraic geometry Scheme theory
Wikipage page ID	18829483 (xsd:integer)
Wikipage revision ID	1095481873 (xsd:integer)
Link from a Wikipage to another Wikipage	Deformation theory Unital ring Ringed space Mathematics Commutative ring Ideal (ring theory) Spectrum of a ring Linear topology Algebraic geometry Base (topology) Nicolas Bourbaki Formal holomorphic function Algebraic geometry T Theorem on formal functions Scheme theory Scheme (mathematics) Completion (ring theory) Schlessinger's theorem Field of fractions Topological ring Noetherian scheme Topological space
Link from a Wikipage to an external page	https://mathoverflow.net/q/27708
sameAs	Formal scheme Formal scheme Formal scheme Formal scheme Formal scheme
dbp:wikiPageUsesTemplate	dbt:Short_description dbt:EGA
has abstract	In der algebraischen Geometrie ist ein formales Schema eine Verallgemeinerung eines Schemas. Grob gesagt beschreibt ein formales Schema eine infinitesimale Umgebung eines Schemas. Formale Schemata finden Anwendung in der und . Es gibt verschiedene Definitionen in der Literatur, häufig werden aus technischen Gründen lediglich lokal noethersche formale Schemata definiert. (de) In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes. A locally Noetherian scheme is a locally Noetherian formal scheme in the canonical way: the formal completion along itself. In other words, the category of locally Noetherian formal schemes contains all locally Noetherian schemes. Formal schemes were motivated by and generalize Zariski's theory of formal holomorphic functions. Algebraic geometry based on formal schemes is called formal algebraic geometry. (en) 대수기하학에서 형식적 스킴(形式的scheme, 영어: formal scheme)은 스스로의 ‘무한소 근방’의 데이터를 기억하는, 스킴의 개념의 일반화이다.:190–200, §Ⅱ.9 (ko)
gold:hypernym	Space
prov:wasDerivedFrom	wikipedia-en:Formal_scheme?oldid=1095481873&ns=0
page length (characters) of wiki page	6112 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Formal_scheme
is Link from a Wikipage to another Wikipage of	Deformation (mathematics) Ind-scheme Timeline of category theory and related mathematics Glossary of algebraic geometry Crystalline cohomology Completion of a ring Functor represented by a scheme Stack (mathematics) Algebraic geometry Formal group law Formal holomorphic function Formal moduli Moduli space Rigid analytic space Noetherian scheme Formal algebraic geometry Formal completion Formal geometry Formal spectrum of a ring Adic morphism Locally noetherian formal scheme
is Wikipage redirect of	Formal algebraic geometry Formal completion Formal geometry Formal spectrum of a ring Adic morphism Locally noetherian formal scheme
is foaf:primaryTopic of	wikipedia-en:Formal_scheme

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