About: Function field (scheme theory)

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The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U. Despite its name, KX does not always give a field for a general scheme X.

Attributes	Values
rdfs:label	Function field (scheme theory) (en) 函数体 (スキーム論) (ja) Corpo de funções (teoria de esquemas) (pt)
rdfs:comment	The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U. Despite its name, KX does not always give a field for a general scheme X. (en) スキーム X の有理函数体の層(sheaf of rational functions) KX は、古典的な代数幾何学での代数多様体の函数体の考え方のスキーム論への一般化である。多様体の場合には、そのような層が、各々の開集合 U へ開集合上の全ての有理函数の環を関連付ける、言い換えると、KX(U) は U 上の正則函数(regular function)の分数の集合である。この「函数体」という名前にもかかわらず、一般的なスキームの場合には、KX は、必ずしも体であるとは限らない。 (ja) Em geometria algébrica, o corpo de funções KX de um esquema X é uma generalização da noção de um feixe de funções racionais sobre uma variedade. No caso de variedades, tal como um feixe associado a cada conjunto aberto U o anel de todas as funções racionais sobre este conjunto aberto; em outras palavras, KX(U) é o conjunto de frações de funções regulares sobre U. Apesar deste nome, KX nem sempre dá um corpo para um esquema geral X. (pt)
dcterms:subject	Scheme theory
Wikipage page ID	381301 (xsd:integer)
Wikipage revision ID	1106966955 (xsd:integer)
Link from a Wikipage to another Wikipage	Generic point Constant sheaf Dense set Zero divisor Function field of an algebraic variety Total quotient ring Local ring Algebraic curve Algebraic geometry Algebraic variety Field (mathematics) Rational function Regular function Ring (mathematics) Birational geometry Scheme theory Field of fractions Glossary of scheme theory Scheme theory Scheme (mathematics) Field of fractions Transcendence degree
Link from a Wikipage to an external page	https://www.e-periodica.ch/cntmng%3Fpid=ens-001:1979:25::101
sameAs	Function field (scheme theory) Function field (scheme theory) Function field (scheme theory) Function field (scheme theory) Function field (scheme theory)
has abstract	The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U. Despite its name, KX does not always give a field for a general scheme X. (en) スキーム X の有理函数体の層(sheaf of rational functions) KX は、古典的な代数幾何学での代数多様体の函数体の考え方のスキーム論への一般化である。多様体の場合には、そのような層が、各々の開集合 U へ開集合上の全ての有理函数の環を関連付ける、言い換えると、KX(U) は U 上の正則函数(regular function)の分数の集合である。この「函数体」という名前にもかかわらず、一般的なスキームの場合には、KX は、必ずしも体であるとは限らない。 (ja) Em geometria algébrica, o corpo de funções KX de um esquema X é uma generalização da noção de um feixe de funções racionais sobre uma variedade. No caso de variedades, tal como um feixe associado a cada conjunto aberto U o anel de todas as funções racionais sobre este conjunto aberto; em outras palavras, KX(U) é o conjunto de frações de funções regulares sobre U. Apesar deste nome, KX nem sempre dá um corpo para um esquema geral X. (pt)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:Function_field_(scheme_theory)?oldid=1106966955&ns=0
page length (characters) of wiki page	4043 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Function_field_(scheme_theory)
is Link from a Wikipage to another Wikipage of	Algebraic cycle Algebraic function field Glossary of algebraic geometry Function field of an algebraic variety Functor represented by a scheme Function field Algebraic curve Function field of a scheme
is Wikipage redirect of	Function field of a scheme
is foaf:primaryTopic of	wikipedia-en:Function_field_(scheme_theory)

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