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- Algebraic_cycle abstract "In mathematics, an algebraic cycle on an algebraic variety V is, roughly speaking, a homology class on V that is represented by a linear combination of subvarieties of V. Therefore, the algebraic cycles on V are the part of the algebraic topology of V that is directly accessible in algebraic geometry. With the formulation of some fundamental conjectures in the 1950s and 1960s, the study of algebraic cycles became one of the main objectives of the algebraic geometry of general varieties.The nature of the difficulties is quite plain: the existence of algebraic cycles is easy to predict, but the current methods of constructing them are deficient. The major conjectures on algebraic cycles include the Hodge conjecture and the Tate conjecture. In the search for a proof of the Weil conjectures, Alexander Grothendieck and Enrico Bombieri formulated what are now known as the standard conjectures of algebraic cycle theory. Algebraic cycles have also been shown to be closely connected with algebraic K-theory.For the purposes of a well-working intersection theory, one uses various equivalence relations on algebraic cycles. Particularly important is the so-called rational equivalence. Cycles up to rational equivalence form a graded ring, the Chow ring, whose multiplication is given by the intersection product. Further fundamental relations include algebraic equivalence, numerical equivalence, and homological equivalence. They have (partly conjectural) applications in the theory of motives.".
- Algebraic_cycle wikiPageID "9520954".
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- Algebraic_cycle wikiPageOutDegree "33".
- Algebraic_cycle wikiPageRevisionID "680674567".
- Algebraic_cycle wikiPageWikiLink Adequate_equivalence_relation.
- Algebraic_cycle wikiPageWikiLink Alexander_Grothendieck.
- Algebraic_cycle wikiPageWikiLink Algebraic_K-theory.
- Algebraic_cycle wikiPageWikiLink Algebraic_geometry.
- Algebraic_cycle wikiPageWikiLink Algebraic_topology.
- Algebraic_cycle wikiPageWikiLink Algebraic_variety.
- Algebraic_cycle wikiPageWikiLink Category:Algebraic_geometry.
- Algebraic_cycle wikiPageWikiLink Chow_ring.
- Algebraic_cycle wikiPageWikiLink Closed_subscheme.
- Algebraic_cycle wikiPageWikiLink Divisor_(algebraic_geometry).
- Algebraic_cycle wikiPageWikiLink Enrico_Bombieri.
- Algebraic_cycle wikiPageWikiLink Equivalence_relations_on_algebraic_cycles.
- Algebraic_cycle wikiPageWikiLink Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete.
- Algebraic_cycle wikiPageWikiLink Finite_morphism.
- Algebraic_cycle wikiPageWikiLink Flat_morphism.
- Algebraic_cycle wikiPageWikiLink Function_field_(scheme_theory).
- Algebraic_cycle wikiPageWikiLink Generic_point.
- Algebraic_cycle wikiPageWikiLink Glossary_of_algebraic_geometry.
- Algebraic_cycle wikiPageWikiLink Hodge_conjecture.
- Algebraic_cycle wikiPageWikiLink Homology_(mathematics).
- Algebraic_cycle wikiPageWikiLink Homology_class.
- Algebraic_cycle wikiPageWikiLink Intersection_product.
- Algebraic_cycle wikiPageWikiLink Intersection_theory.
- Algebraic_cycle wikiPageWikiLink Irreducible_component.
- Algebraic_cycle wikiPageWikiLink Mathematics.
- Algebraic_cycle wikiPageWikiLink Motive_(algebraic_geometry).
- Algebraic_cycle wikiPageWikiLink Proper_morphism.
- Algebraic_cycle wikiPageWikiLink Reduced_scheme.
- Algebraic_cycle wikiPageWikiLink Scheme_(mathematics).
- Algebraic_cycle wikiPageWikiLink Springer-Verlag.
- Algebraic_cycle wikiPageWikiLink Springer_Science+Business_Media.
- Algebraic_cycle wikiPageWikiLink Standard_conjectures_on_algebraic_cycles.
- Algebraic_cycle wikiPageWikiLink Subvarieties.
- Algebraic_cycle wikiPageWikiLink Tate_conjecture.
- Algebraic_cycle wikiPageWikiLink Weil_conjectures.
- Algebraic_cycle wikiPageWikiLink Zariski_topology.
- Algebraic_cycle wikiPageWikiLinkText "Algebraic cycle".
- Algebraic_cycle wikiPageWikiLinkText "algebraic cycle".
- Algebraic_cycle wikiPageWikiLinkText "cycle".
- Algebraic_cycle wikiPageWikiLinkText "cycles".
- Algebraic_cycle hasPhotoCollection Algebraic_cycle.
- Algebraic_cycle wikiPageUsesTemplate Template:Citation.
- Algebraic_cycle subject Category:Algebraic_geometry.
- Algebraic_cycle hypernym Part.
- Algebraic_cycle type Article.
- Algebraic_cycle type Article.
- Algebraic_cycle comment "In mathematics, an algebraic cycle on an algebraic variety V is, roughly speaking, a homology class on V that is represented by a linear combination of subvarieties of V. Therefore, the algebraic cycles on V are the part of the algebraic topology of V that is directly accessible in algebraic geometry.".
- Algebraic_cycle label "Algebraic cycle".
- Algebraic_cycle sameAs Algebraiske_cyklus.
- Algebraic_cycle sameAs Cycle_(géométrie_algébrique).
- Algebraic_cycle sameAs 代数的サイクル.
- Algebraic_cycle sameAs 대수적_순환.
- Algebraic_cycle sameAs m.02phngq.
- Algebraic_cycle sameAs Q4723996.
- Algebraic_cycle sameAs Q4723996.
- Algebraic_cycle wasDerivedFrom Algebraic_cycle?oldid=680674567.
- Algebraic_cycle isPrimaryTopicOf Algebraic_cycle.