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- Adequate_equivalence_relation abstract "In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives. For every adequate equivalence relation, one may define the category of pure motives with respect to that relation.Possible (and useful) adequate equivalence relations include rational, algebraic, homological and numerical equivalence. They are called \"adequate\" because dividing out by the equivalence relation is functorial, i.e. push-forward (with change of co-dimension) and pull-back of cycles is well-defined. Codimension one cycles modulo rational equivalence form the classical group of divisors. All cycles modulo rational equivalence form the Chow ring.".
- Adequate_equivalence_relation wikiPageID "25384599".
- Adequate_equivalence_relation wikiPageLength "5681".
- Adequate_equivalence_relation wikiPageOutDegree "21".
- Adequate_equivalence_relation wikiPageRevisionID "672566403".
- Adequate_equivalence_relation wikiPageWikiLink Algebraic_cycle.
- Adequate_equivalence_relation wikiPageWikiLink Algebraic_geometry.
- Adequate_equivalence_relation wikiPageWikiLink Category:Algebraic_geometry.
- Adequate_equivalence_relation wikiPageWikiLink Chow_ring.
- Adequate_equivalence_relation wikiPageWikiLink Chows_moving_lemma.
- Adequate_equivalence_relation wikiPageWikiLink Correspondence_(mathematics).
- Adequate_equivalence_relation wikiPageWikiLink Curve.
- Adequate_equivalence_relation wikiPageWikiLink Divisor_(algebraic_geometry).
- Adequate_equivalence_relation wikiPageWikiLink Equivalence_relation.
- Adequate_equivalence_relation wikiPageWikiLink Flat_morphism.
- Adequate_equivalence_relation wikiPageWikiLink Griffiths_group.
- Adequate_equivalence_relation wikiPageWikiLink Intersection_theory.
- Adequate_equivalence_relation wikiPageWikiLink Mathematics.
- Adequate_equivalence_relation wikiPageWikiLink Motive_(algebraic_geometry).
- Adequate_equivalence_relation wikiPageWikiLink Néron–Severi_group.
- Adequate_equivalence_relation wikiPageWikiLink Pierre_Samuel.
- Adequate_equivalence_relation wikiPageWikiLink Projective_line.
- Adequate_equivalence_relation wikiPageWikiLink Projective_variety.
- Adequate_equivalence_relation wikiPageWikiLink Standard_conjectures_on_algebraic_cycles.
- Adequate_equivalence_relation wikiPageWikiLink Weil_cohomology_theory.
- Adequate_equivalence_relation wikiPageWikiLinkText "Adequate equivalence relation".
- Adequate_equivalence_relation wikiPageWikiLinkText "adequate equivalence relation".
- Adequate_equivalence_relation wikiPageWikiLinkText "equivalence relations".
- Adequate_equivalence_relation wikiPageWikiLinkText "numerical equivalence".
- Adequate_equivalence_relation wikiPageUsesTemplate Template:Citation.
- Adequate_equivalence_relation subject Category:Algebraic_geometry.
- Adequate_equivalence_relation hypernym Relation.
- Adequate_equivalence_relation type Agent.
- Adequate_equivalence_relation comment "In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Pierre Samuel formalized the concept of an adequate equivalence relation in 1958. Since then it has become central to theory of motives.".
- Adequate_equivalence_relation label "Adequate equivalence relation".
- Adequate_equivalence_relation sameAs Q4682344.
- Adequate_equivalence_relation sameAs m.02qf2bp.
- Adequate_equivalence_relation sameAs Q4682344.
- Adequate_equivalence_relation wasDerivedFrom Adequate_equivalence_relation?oldid=672566403.
- Adequate_equivalence_relation isPrimaryTopicOf Adequate_equivalence_relation.