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In mathematics, a Weil group, introduced by Weil, is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF. There also exists "finite level" modifications of the Galois groups: if E/F is a finite extension, then the relative Weil group of E/F is WE/F = WF/W cE (where the superscript c denotes the commutator subgroup). For more details about Weil groups see or or.

Attributes	Values
rdf:type	video game
rdfs:label	Weil group (en) ヴェイユ群 (ja)
rdfs:comment	In mathematics, a Weil group, introduced by Weil, is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF. There also exists "finite level" modifications of the Galois groups: if E/F is a finite extension, then the relative Weil group of E/F is WE/F = WF/W cE (where the superscript c denotes the commutator subgroup). For more details about Weil groups see or or. (en) 数学において、ヴェイユ群(Weil group)は、 Weilで導入され、類体論で使われる絶対ガロア群の局所体や大域体での変形である。そのような体 F に対して、ヴェイユ群は一般に WF と記される。ガロア群の「有限なレベル」の変形も存在し、E/F を有限拡大としたときの E/F の相対ヴェイユ群(relative Weil group)が WE/F = WF/W cE である（この記号 c は交換子部分群による完備化を意味している。）。ヴェイユ群について、詳しくは、ややを参照。 (ja)
dcterms:subject	Class field theory
Wikipage page ID	6375618 (xsd:integer)
Wikipage revision ID	1045234099 (xsd:integer)
Link from a Wikipage to another Wikipage	Commutator subgroup Fundamental class Langlands group Langlands program Local field Locally profinite group American Mathematical Society Finite extension Global field Group cohomology Class field theory Absolute Galois group Class field theory Class formation Infinite cyclic Shafarevich–Weil theorem Frobenius automorphism Springer-Verlag Arithmetic Frobenius Local Langlands correspondence Weil–Deligne representation
Link from a Wikipage to an external page	http://www.ams.org/bookstore-getitem/item=chel-366-h http://www.ams.org/online_bks/pspum332/
sameAs	Weil group Weil group Weil group Weil group
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:Harvtxt dbt:Other_uses dbt:Reflist dbt:Isbn dbt:Harvs dbt:SubSup
has abstract	In mathematics, a Weil group, introduced by Weil, is a modification of the absolute Galois group of a local or global field, used in class field theory. For such a field F, its Weil group is generally denoted WF. There also exists "finite level" modifications of the Galois groups: if E/F is a finite extension, then the relative Weil group of E/F is WE/F = WF/W cE (where the superscript c denotes the commutator subgroup). For more details about Weil groups see or or. (en) 数学において、ヴェイユ群(Weil group)は、 Weilで導入され、類体論で使われる絶対ガロア群の局所体や大域体での変形である。そのような体 F に対して、ヴェイユ群は一般に WF と記される。ガロア群の「有限なレベル」の変形も存在し、E/F を有限拡大としたときの E/F の相対ヴェイユ群(relative Weil group)が WE/F = WF/W cE である（この記号 c は交換子部分群による完備化を意味している。）。ヴェイユ群について、詳しくは、ややを参照。 (ja)
gold:hypernym	Modification
prov:wasDerivedFrom	wikipedia-en:Weil_group?oldid=1045234099&ns=0
page length (characters) of wiki page	7731 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weil_group
is differentFrom of	Weil–Châtelet group
is Link from a Wikipage to another Wikipage of	Timeline of class field theory Lafforgue's theorem André Weil Langlands classification Langlands dual group Langlands group Langlands–Deligne local constant Local Langlands conjectures Locally profinite group Field (mathematics) Basic Number Theory Pierre Deligne Séminaire Nicolas Bourbaki (1960–1969) List of things named after André Weil Weil-Deligne group Weil-Deligne group scheme Weil group of a class formation Weil–Deligne group Weil–Deligne group scheme
is Wikipage redirect of	Weil-Deligne group Weil-Deligne group scheme Weil group of a class formation Weil–Deligne group Weil–Deligne group scheme
is known for of	André Weil
is foaf:primaryTopic of	wikipedia-en:Weil_group

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