About: Class formation

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In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that appear in class field theory.

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rdf:type	Band
rdfs:label	Class formation (en) Formation de classes (fr)
rdfs:comment	In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that appear in class field theory. (en) En mathématiques, une formation de classes est une structure utilisée pour organiser les divers groupes de Galois et les modules qui apparaissent dans la théorie des corps de classes. Ils ont été inventées par Emil Artin et John Tate. (fr)
dcterms:subject	Algebraic number theory Class field theory
Wikipage page ID	6019404 (xsd:integer)
Wikipage revision ID	1045234068 (xsd:integer)
Link from a Wikipage to another Wikipage	Module (mathematics) Mordell–Weil group John Tate (mathematician) Riemann zeta function Dedekind zeta function Profinite group Lubin–Tate formal group law Claude Chevalley Emil Artin Complex multiplication Function field of an algebraic variety Kronecker–Weber theorem Topological group G-module Galois cohomology Galois group Hasse norm theorem Langlands program Local class field theory American Mathematical Society Cyclic group Brauer group Chebotarev's density theorem Dirichlet density Hilbert class field Hilbert's theorem 90 Tate cohomology group Abelian extension Algebraic number theory Class field theory Herbrand quotient Artin L-function Class field theory Idele Takagi existence theorem Weyl group Weil–Châtelet group Kummer extension Springer-Verlag Tate's theorem Artin reciprocity Artin–Schreier extension Chebotarev
Link from a Wikipage to an external page	https://www.ams.org/online_bks/pspum332/ https://books.google.com/books%3Fisbn=978-0-8218-4426-7
sameAs	Class formation Class formation Class formation Class formation
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Div_col dbt:Div_col_end dbt:Harvtxt dbt:ISBN dbt:Main
has abstract	In mathematics, a class formation is a topological group acting on a module satisfying certain conditions. Class formations were introduced by Emil Artin and John Tate to organize the various Galois groups and modules that appear in class field theory. (en) En mathématiques, une formation de classes est une structure utilisée pour organiser les divers groupes de Galois et les modules qui apparaissent dans la théorie des corps de classes. Ils ont été inventées par Emil Artin et John Tate. Plus précisément, c'est la donnée d'un groupe, agissant sur un certain module, le tout vérifiant une certaine axiomatique, principalement exprimée d'un point de vue cohomologique. Le but de cette notion est d'axiomatiser la théorie des corps de classes, indépendamment des divers contextes où on souhaite obtenir ses énoncés : corps fini ou infini, global ou local, de caractéristique nulle ou positive. Le groupe considéré étant alors le groupe de Galois absolu du corps considéré, et le module étant le groupe multiplicatif de la clôture séparable de ce même corps. (fr)
gold:hypernym	Group
prov:wasDerivedFrom	wikipedia-en:Class_formation?oldid=1045234068&ns=0
page length (characters) of wiki page	18338 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Class_formation
is Link from a Wikipage to another Wikipage of	Timeline of class field theory Galois cohomology Galois module Group cohomology Tate cohomology group Herbrand quotient Artin reciprocity law Class field theory Form class Formation Takagi existence theorem Weil group Field formation First inequality of class field theory Second inequality of class field theory
is Wikipage redirect of	Field formation First inequality of class field theory Second inequality of class field theory
is Wikipage disambiguates of	Formation
is foaf:primaryTopic of	wikipedia-en:Class_formation

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