About: Mumford–Tate group

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In algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle group, over the rational numbers. Mumford introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. introduced the p-adic analogue of Mumford's construction for Hodge–Tate modules, using the work of Tate on p-divisible groups, and named them Mumford–Tate groups.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Group100031264 device yago:WikicatAlgebraicGroups
rdfs:label	Mumford–Tate group (en)
rdfs:comment	In algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle group, over the rational numbers. Mumford introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. introduced the p-adic analogue of Mumford's construction for Hodge–Tate modules, using the work of Tate on p-divisible groups, and named them Mumford–Tate groups. (en)
dcterms:subject	Hodge theory Algebraic groups
Wikipage page ID	27137708 (xsd:integer)
Wikipage revision ID	1076649568 (xsd:integer)
Link from a Wikipage to another Wikipage	Sato–Tate conjecture Multiplicative group Motivic Galois group Algebraic group Algebraic torus Hodge theory Algebraic groups Lie algebra Zariski closure Algebraic geometry American Mathematical Society Weil restriction Abelian variety Hodge structure Hodge–Tate module Phillip Griffiths Pierre Deligne Circle group Kähler manifold Rational numbers Unitary group P-divisible group Transcendence degree Rational representation Tate module L-adic Springer-Verlag Galois representation Period matrix Cohomology group Lattice (group theory)
Link from a Wikipage to an external page	http://www.math.umass.edu/~hacking/agnes/griffiths.pdf http://www.cms.zju.edu.cn/UploadFiles/AttachFiles/2005730145725232.pdf
sameAs	Mumford–Tate group Mumford–Tate group Mumford–Tate group
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Reflist dbt:Short_description dbt:Harvs
has abstract	In algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given by a rational representation of an algebraic torus, the definition of G is as the Zariski closure of the image in the representation of the circle group, over the rational numbers. Mumford introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. introduced the p-adic analogue of Mumford's construction for Hodge–Tate modules, using the work of Tate on p-divisible groups, and named them Mumford–Tate groups. (en)
gold:hypernym	G
prov:wasDerivedFrom	wikipedia-en:Mumford–Tate_group?oldid=1076649568&ns=0
page length (characters) of wiki page	6181 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Mumford–Tate_group
is Link from a Wikipage to another Wikipage of	Motive (algebraic geometry) Hodge group John Tate (mathematician) Schanuel's conjecture Mumford-Tate group 1966 in science Linear algebraic group Weil restriction Hodge–Tate module List of things named after Alexander Grothendieck List of things named after W. V. D. Hodge Tate group Serre group Tannakian formalism Mumford-Tate conjecture Mumford–Tate conjecture
is Wikipage redirect of	Hodge group Mumford-Tate group Mumford-Tate conjecture Mumford–Tate conjecture
is foaf:primaryTopic of	wikipedia-en:Mumford–Tate_group

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