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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:award
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1 million USD
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gptkbp:concerns
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Kähler manifolds
algebraic cycles
Hodge classes
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gptkbp:difficulty
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very high
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gptkbp:field
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gptkb:algebraic_geometry
gptkb:topology
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gptkbp:hasApplication
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gptkb:algebraic_geometry
number theory
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gptkbp:hasCounterexamplesIn
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non-projective varieties
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gptkbp:hasNoCounterexamplesIn
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projective varieties
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gptkbp:hasPartialResults
|
true
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gptkbp:importantFor
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high
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gptkbp:isOneOf
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gptkb:Millennium_Prize_Problems
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gptkbp:offeredBy
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gptkb:Clay_Mathematics_Institute
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gptkbp:proposedBy
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gptkb:W._V._D._Hodge
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gptkbp:relatedTo
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gptkb:topology
gptkb:Hodge_theory
gptkb:de_Rham_cohomology
complex algebraic varieties
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gptkbp:sentence
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Every Hodge class on a non-singular projective complex algebraic variety is a rational linear combination of the cohomology classes of algebraic cycles.
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gptkbp:status
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open
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gptkbp:yearProposed
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1941
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gptkbp:bfsParent
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gptkb:Clay_Mathematics_Institute_Millennium_Prize_Problems
gptkb:Clay_Millennium_Prize_Problem
gptkb:Clay_Millennium_Prize
gptkb:Clay_Mathematics_Institute_Millennium_Prize
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gptkbp:bfsLayer
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7
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https://www.w3.org/2000/01/rdf-schema#label
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Hodge Conjecture
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