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In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:WikicatTopologicalMethodsOfAlgebraicGeometry yago:Ability105616246 yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:Know-how105616786 yago:Method105660268 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	テイト予想 (代数幾何学) (ja) Tate conjecture (en)
rdfs:comment	In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture. (en) 数論および代数幾何学において、テイト予想（テイトよそう、英: Tate conjecture）は、ジョン・テイト (John Tate) による1963年の予想であり、代数多様体上の代数的サイクルをより計算可能な不変量であるエタールコホモロジー上のガロワ加群のことばで記述するものであった。テイト予想は代数的サイクルの理論において中心的な問題である。予想はホッジ予想の数論的類似物と考えることができる。 (ja)
name	Tate conjecture (en)
foaf:depiction
dct:subject	Conjectures Topological methods of algebraic geometry Diophantine geometry Unsolved problems in number theory
Wikipage page ID	3124804 (xsd:integer)
Wikipage revision ID	1059600943 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime field Mordell conjecture Birch and Swinnerton-Dyer conjecture Algebraic closure Algebraic cycle Hodge conjecture John Tate (mathematician) Inventiones Mathematicae Jacobian variety Numerical equivalence L-adic number Conjectures Gerd Faltings Conjecture Topological methods of algebraic geometry Standard conjectures on algebraic cycles Étale cohomology Function field of an algebraic variety Galois module Irreducible representation James Milne (mathematician) Hasse-Weil zeta function Algebraic geometry Algebraic variety Cyclotomic character Field (mathematics) Diophantine geometry Abelian varieties Number theory P-adic integer Lefschetz theorem on (1,1)-classes Projective variety Isogeny Prime number Abelian variety Unsolved problems in number theory Absolute Galois group K3 surface Codimension Picard group Arthur Ogus Group representation Smooth scheme Tate module Tate twist L-adic cohomology
Link from a Wikipage to an external page	http://www.jmilne.org/math/articles/2007e.pdf
sameAs	Tate conjecture Tate conjecture Tate conjecture Tate conjecture Tate conjecture
dbp:wikiPageUsesTemplate	dbt:Infobox_mathematical_statement dbt:Citation dbt:Harvtxt dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/John_Tate.jpg?width=300
caption	John Tate in 1993 (en)
field	Algebraic geometry and number theory (en)
consequences	Standard conjectures on algebraic cycles
has abstract	In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture. (en) 数論および代数幾何学において、テイト予想（テイトよそう、英: Tate conjecture）は、ジョン・テイト (John Tate) による1963年の予想であり、代数多様体上の代数的サイクルをより計算可能な不変量であるエタールコホモロジー上のガロワ加群のことばで記述するものであった。テイト予想は代数的サイクルの理論において中心的な問題である。予想はホッジ予想の数論的類似物と考えることができる。 (ja)
conjecture date	1963 (xsd:integer)
conjectured by	John Tate (mathematician)
known cases	divisors on abelian varieties (en)
gold:hypernym	Conjecture
prov:wasDerivedFrom	wikipedia-en:Tate_conjecture?oldid=1059600943&ns=0
page length (characters) of wiki page	9703 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tate_conjecture
is Link from a Wikipage to another Wikipage of	List of conjectures Motive (algebraic geometry) Algebraic cycle Hodge conjecture John Tate (mathematician) Deaths in October 2019

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