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- Motive_(algebraic_geometry) abstract "In algebraic geometry, a motive (or sometimes motif, following French usage) denotes 'some essential part of an algebraic variety'. To date, pure motives have been defined, while conjectural mixed motives have not.[citation needed] Pure motives are triples (X, p, m), where X is a smooth projective variety, p : X ⊢ X is an idempotent correspondence, and m an integer. A morphism from (X, p, m) to (Y, q, n) is given by a correspondence of degree n – m.As far as mixed motives, following Alexander Grothendieck, mathematicians are working to find a suitable definition which will then provide a "universal" cohomology theory. In terms of category theory, it was intended to have a definition via splitting idempotents in a category of algebraic correspondences. The way ahead for that definition has been blocked for some decades by the failure to prove the standard conjectures on algebraic cycles. This prevents the category from having 'enough' morphisms, as can currently be shown.[citation needed] While the category of motives was supposed to be the universal Weil cohomology much discussed in the years 1960-1970, that hope for it remains unfulfilled. On the other hand, by a quite different route, motivic cohomology now has a technically adequate definition.".
- Motive_(algebraic_geometry) wikiPageExternalLink motiviclectures.html.
- Motive_(algebraic_geometry) wikiPageExternalLink what-is.pdf.
- Motive_(algebraic_geometry) wikiPageExternalLink MOT.pdf.
- Motive_(algebraic_geometry) wikiPageExternalLink 0368.
- Motive_(algebraic_geometry) wikiPageExternalLink 0832.
- Motive_(algebraic_geometry) wikiPageID "430680".
- Motive_(algebraic_geometry) wikiPageRevisionID "606104329".
- Motive_(algebraic_geometry) hasPhotoCollection Motive_(algebraic_geometry).
- Motive_(algebraic_geometry) subject Category:Algebraic_geometry.
- Motive_(algebraic_geometry) subject Category:Homological_algebra.
- Motive_(algebraic_geometry) subject Category:Topological_methods_of_algebraic_geometry.
- Motive_(algebraic_geometry) type Ability105616246.
- Motive_(algebraic_geometry) type Abstraction100002137.
- Motive_(algebraic_geometry) type Cognition100023271.
- Motive_(algebraic_geometry) type Know-how105616786.
- Motive_(algebraic_geometry) type Method105660268.
- Motive_(algebraic_geometry) type PsychologicalFeature100023100.
- Motive_(algebraic_geometry) type TopologicalMethodsOfAlgebraicGeometry.
- Motive_(algebraic_geometry) comment "In algebraic geometry, a motive (or sometimes motif, following French usage) denotes 'some essential part of an algebraic variety'. To date, pure motives have been defined, while conjectural mixed motives have not.[citation needed] Pure motives are triples (X, p, m), where X is a smooth projective variety, p : X ⊢ X is an idempotent correspondence, and m an integer.".
- Motive_(algebraic_geometry) label "Motif (géométrie algébrique)".
- Motive_(algebraic_geometry) label "Motive (algebraic geometry)".
- Motive_(algebraic_geometry) label "モチーフ (数学)".
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- Motive_(algebraic_geometry) sameAs モチーフ_(数学).
- Motive_(algebraic_geometry) sameAs 모티브_(수학).
- Motive_(algebraic_geometry) sameAs m.027n21.
- Motive_(algebraic_geometry) sameAs Q840594.
- Motive_(algebraic_geometry) sameAs Q840594.
- Motive_(algebraic_geometry) sameAs Motive_(algebraic_geometry).
- Motive_(algebraic_geometry) wasDerivedFrom Motive_(algebraic_geometry)?oldid=606104329.
- Motive_(algebraic_geometry) isPrimaryTopicOf Motive_(algebraic_geometry).