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- Hodge_conjecture abstract "The Hodge conjecture is a major unsolved problem in algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they are sums of Poincaré duals of the homology classes of subvarieties. It was formulated by the Scottish mathematician William Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of de Rham cohomology to include extra structure that is present in the case of complex algebraic varieties. It received little attention before Hodge presented it in an address during the 1950 International Congress of Mathematicians, held in Cambridge, Massachusetts, U.S. The Hodge conjecture is one of the Clay Mathematics Institute's Millennium Prize Problems, with a prize of $1,000,000 for whoever can prove or disprove the Hodge conjecture.".
- Hodge_conjecture wikiPageExternalLink CM_1977__34_2_199_0.pdf.
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- Hodge_conjecture wikiPageExternalLink why-believe-the-hodge-conjecture.
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- Hodge_conjecture wikiPageExternalLink hodge.pdf.
- Hodge_conjecture wikiPageExternalLink netscape_noframes.html.
- Hodge_conjecture wikiPageExternalLink hodgeloci.pdf.
- Hodge_conjecture wikiPageID "244518".
- Hodge_conjecture wikiPageLength "18822".
- Hodge_conjecture wikiPageOutDegree "65".
- Hodge_conjecture wikiPageRevisionID "681113842".
- Hodge_conjecture wikiPageWikiLink Abelian_variety.
- Hodge_conjecture wikiPageWikiLink Algebraic_cycle.
- Hodge_conjecture wikiPageWikiLink Algebraic_geometry.
- Hodge_conjecture wikiPageWikiLink Algebraic_geometry_and_analytic_geometry.
- Hodge_conjecture wikiPageWikiLink Algebraic_topology.
- Hodge_conjecture wikiPageWikiLink Algebraic_variety.
- Hodge_conjecture wikiPageWikiLink Burt_Totaro.
- Hodge_conjecture wikiPageWikiLink Cap_product.
- Hodge_conjecture wikiPageWikiLink Category:Algebraic_geometry.
- Hodge_conjecture wikiPageWikiLink Category:Conjectures.
- Hodge_conjecture wikiPageWikiLink Category:Hodge_theory.
- Hodge_conjecture wikiPageWikiLink Category:Homology_theory.
- Hodge_conjecture wikiPageWikiLink Category:Millennium_Prize_Problems.
- Hodge_conjecture wikiPageWikiLink Chern_class.
- Hodge_conjecture wikiPageWikiLink Claire_Voisin.
- Hodge_conjecture wikiPageWikiLink Clay_Mathematics_Institute.
- Hodge_conjecture wikiPageWikiLink Cobordism.
- Hodge_conjecture wikiPageWikiLink Cohomology.
- Hodge_conjecture wikiPageWikiLink Compact_space.
- Hodge_conjecture wikiPageWikiLink Complex_manifold.
- Hodge_conjecture wikiPageWikiLink Complex_multiplication.
- Hodge_conjecture wikiPageWikiLink Complex_number.
- Hodge_conjecture wikiPageWikiLink Complex_projective_space.
- Hodge_conjecture wikiPageWikiLink Cup_product.
- Hodge_conjecture wikiPageWikiLink De_Rham_cohomology.
- Hodge_conjecture wikiPageWikiLink Differentiable_manifold.
- Hodge_conjecture wikiPageWikiLink Differential_form.
- Hodge_conjecture wikiPageWikiLink Divisor_(algebraic_geometry).
- Hodge_conjecture wikiPageWikiLink Exponential_exact_sequence.
- Hodge_conjecture wikiPageWikiLink Exponential_sheaf_sequence.
- Hodge_conjecture wikiPageWikiLink Fourfold.
- Hodge_conjecture wikiPageWikiLink Fubini–Study_metric.
- Hodge_conjecture wikiPageWikiLink Fundamental_class.
- Hodge_conjecture wikiPageWikiLink Griffiths_transversality_theorem.
- Hodge_conjecture wikiPageWikiLink Hard_Lefschetz_theorem.
- Hodge_conjecture wikiPageWikiLink Harmonic_form.
- Hodge_conjecture wikiPageWikiLink Harmonic_function.
- Hodge_conjecture wikiPageWikiLink Henri_Poincaré.
- Hodge_conjecture wikiPageWikiLink Hodge_structure.
- Hodge_conjecture wikiPageWikiLink Hodge_theory.
- Hodge_conjecture wikiPageWikiLink Homology_(mathematics).
- Hodge_conjecture wikiPageWikiLink Homology_class.
- Hodge_conjecture wikiPageWikiLink Hypersurface.
- Hodge_conjecture wikiPageWikiLink Imaginary_quadratic_field.
- Hodge_conjecture wikiPageWikiLink Indranil_Biswas.
- Hodge_conjecture wikiPageWikiLink International_Congress_of_Mathematicians.
- Hodge_conjecture wikiPageWikiLink Journal_of_the_American_Mathematical_Society.
- Hodge_conjecture wikiPageWikiLink K-theory.
- Hodge_conjecture wikiPageWikiLink Kähler_manifold.
- Hodge_conjecture wikiPageWikiLink Lefschetz_hyperplane_theorem.
- Hodge_conjecture wikiPageWikiLink Lefschetz_theorem.
- Hodge_conjecture wikiPageWikiLink Lefschetz_theorem_on_(1,1)-classes.
- Hodge_conjecture wikiPageWikiLink Massachusetts.
- Hodge_conjecture wikiPageWikiLink Mathematische_Annalen.
- Hodge_conjecture wikiPageWikiLink Millennium_Prize_Problems.
- Hodge_conjecture wikiPageWikiLink Non-singular.
- Hodge_conjecture wikiPageWikiLink Normal_function_(geometry).
- Hodge_conjecture wikiPageWikiLink Orientability.
- Hodge_conjecture wikiPageWikiLink Orientable.
- Hodge_conjecture wikiPageWikiLink Period_mapping.
- Hodge_conjecture wikiPageWikiLink Poincaré_duality.
- Hodge_conjecture wikiPageWikiLink Quadratic_field.
- Hodge_conjecture wikiPageWikiLink Quadric.
- Hodge_conjecture wikiPageWikiLink Sheaf_cohomology.
- Hodge_conjecture wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Hodge_conjecture wikiPageWikiLink Smooth_manifold.
- Hodge_conjecture wikiPageWikiLink Tate_conjecture.
- Hodge_conjecture wikiPageWikiLink Topology_(journal).
- Hodge_conjecture wikiPageWikiLink W._V._D._Hodge.
- Hodge_conjecture wikiPageWikiLink Weil_cohomology.
- Hodge_conjecture wikiPageWikiLink Weil_cohomology_theory.
- Hodge_conjecture wikiPageWikiLink William_Vallance_Douglas_Hodge.
- Hodge_conjecture wikiPageWikiLinkText "Hodge conjecture".
- Hodge_conjecture wikiPageWikiLinkText "The Hodge conjecture".
- Hodge_conjecture wikiPageWikiLinkText "The topological invariants of algebraic varieties".
- Hodge_conjecture hasPhotoCollection Hodge_conjecture.
- Hodge_conjecture wikiPageUsesTemplate Template:Citation.
- Hodge_conjecture wikiPageUsesTemplate Template:Citation_needed.
- Hodge_conjecture wikiPageUsesTemplate Template:Harvtxt.
- Hodge_conjecture wikiPageUsesTemplate Template:Millennium_Problems.
- Hodge_conjecture wikiPageUsesTemplate Template:Reflist.
- Hodge_conjecture subject Category:Algebraic_geometry.
- Hodge_conjecture subject Category:Conjectures.
- Hodge_conjecture subject Category:Hodge_theory.
- Hodge_conjecture subject Category:Homology_theory.
- Hodge_conjecture subject Category:Millennium_Prize_Problems.
- Hodge_conjecture hypernym Problem.
- Hodge_conjecture type Article.