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gptkbp:instanceOf
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gptkb:mathematical_concept
|
|
gptkbp:appliesTo
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projective algebraic varieties
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|
gptkbp:award
|
1 million USD
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gptkbp:category
|
Hilbert problem
open problem in mathematics
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|
gptkbp:discusses
|
gptkb:Hodge's_1950_ICM_address
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gptkbp:field
|
gptkb:algebraic_geometry
complex geometry
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gptkbp:hasCounterexamplesIn
|
singular varieties
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|
gptkbp:hasNoCounterexamplesIn
|
smooth projective varieties
|
|
gptkbp:hasPartialResults
|
true
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|
https://www.w3.org/2000/01/rdf-schema#label
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Hodge conjecture
|
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gptkbp:importantFor
|
central in algebraic geometry
|
|
gptkbp:isMillenniumPrizeProblem
|
true
|
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gptkbp:namedAfter
|
gptkb:W._V._D._Hodge
|
|
gptkbp:offeredBy
|
gptkb:Clay_Mathematics_Institute
|
|
gptkbp:proposedBy
|
gptkb:W._V._D._Hodge
|
|
gptkbp:relatedTo
|
gptkb:Hodge_theory
gptkb:Tate_conjecture
gptkb:Standard_conjectures_on_algebraic_cycles
gptkb:de_Rham_cohomology
cohomology
Kähler manifolds
algebraic cycles
|
|
gptkbp:sentence
|
Every Hodge class on a non-singular projective complex algebraic variety is a rational linear combination of classes of algebraic cycles.
|
|
gptkbp:status
|
unsolved
|
|
gptkbp:yearProposed
|
1950
|
|
gptkbp:bfsParent
|
gptkb:William_Vallance_Douglas_Hodge
gptkb:algebraic_geometry
gptkb:Hodge_theory
gptkb:William_V._D._Hodge
gptkb:Tate_conjecture
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|
gptkbp:bfsLayer
|
5
|