gptkbp:instanceOf
|
gptkb:mathematical_concept
|
gptkbp:award
|
1 million USD
|
gptkbp:concerns
|
Kähler manifolds
algebraic cycles
Hodge classes
|
gptkbp:difficulty
|
very high
|
gptkbp:field
|
gptkb:algebraic_geometry
gptkb:topology
|
gptkbp:hasApplication
|
gptkb:algebraic_geometry
number theory
|
gptkbp:hasCounterexamplesIn
|
non-projective varieties
|
gptkbp:hasNoCounterexamplesIn
|
projective varieties
|
gptkbp:hasPartialResults
|
true
|
https://www.w3.org/2000/01/rdf-schema#label
|
Hodge Conjecture
|
gptkbp:importantFor
|
high
|
gptkbp:isOneOf
|
gptkb:Millennium_Prize_Problems
|
gptkbp:offeredBy
|
gptkb:Clay_Mathematics_Institute
|
gptkbp:proposedBy
|
gptkb:W._V._D._Hodge
|
gptkbp:relatedTo
|
gptkb:topology
gptkb:Hodge_theory
gptkb:de_Rham_cohomology
complex algebraic varieties
|
gptkbp:sentence
|
Every Hodge class on a non-singular projective complex algebraic variety is a rational linear combination of the cohomology classes of algebraic cycles.
|
gptkbp:status
|
open
|
gptkbp:yearProposed
|
1941
|
gptkbp:bfsParent
|
gptkb:Clay_Millennium_Prize
|
gptkbp:bfsLayer
|
5
|