Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:challenges |
to prove
|
| gptkbp:field |
algebraic geometry
|
| gptkbp:has_applications_in |
mathematical physics
|
| gptkbp:has_historical_significance |
in the development of algebraic geometry
|
| gptkbp:has_implications_for |
gptkb:topology
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hodge Conjecture
|
| gptkbp:involves |
projective algebraic varieties
|
| gptkbp:is_aimed_at |
understanding algebraic varieties
|
| gptkbp:is_analyzed_in |
advanced mathematics courses
|
| gptkbp:is_associated_with |
Hodge decomposition
the study of differential forms the study of algebraic geometry techniques |
| gptkbp:is_connected_to |
complex geometry
the theory of algebraic varieties the study of complex manifolds the study of cycles |
| gptkbp:is_considered |
a significant challenge in mathematics
a central problem in mathematics one of the seven Millennium Prize Problems a fundamental question in algebraic geometry a key topic in algebraic geometry research a pivotal question in modern mathematics |
| gptkbp:is_discussed_in |
gptkb:academic_journals
gptkb:academic_conferences mathematical literature mathematical seminars online mathematical forums |
| gptkbp:is_examined_in |
gptkb:Mathematician
mathematical research projects topological studies research mathematicians |
| gptkbp:is_explored_in |
research papers
mathematical textbooks computational methods graduate studies various mathematical techniques various mathematical approaches |
| gptkbp:is_influenced_by |
previous mathematical theories
|
| gptkbp:is_influential_in |
gptkb:Physics
modern mathematics the development of mathematical theories. |
| gptkbp:is_linked_to |
gptkb:Riemann_surfaces
the concept of duality the concept of cohomology |
| gptkbp:is_part_of |
theoretical mathematics
theoretical frameworks in mathematics Hodge theory framework the study of algebraic cycles the broader context of mathematical conjectures |
| gptkbp:is_related_to |
algebraic topology
Kähler manifolds the theory of motives |
| gptkbp:is_studied_in |
gptkb:Mathematics
|
| gptkbp:issues |
relationship between algebraic cycles and cohomology classes
|
| gptkbp:proposed_by |
gptkb:W._V._D._Hodge
|
| gptkbp:related_to |
Hodge theory
|
| gptkbp:bfsParent |
gptkb:Millennium_Prize_Problems
|
| gptkbp:bfsLayer |
6
|