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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. 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. 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.
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- Motive_(algebraic_geometry) wikiPageRevisionID "653889258".
- Motive_(algebraic_geometry) wikiPageWikiLink Adequate_equivalence_relation.
- Motive_(algebraic_geometry) wikiPageWikiLink Affine_space.
- Motive_(algebraic_geometry) wikiPageWikiLink Alexander_Beilinson.
- Motive_(algebraic_geometry) wikiPageWikiLink Alexander_Grothendieck.
- Motive_(algebraic_geometry) wikiPageWikiLink Algebraic_K-theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Algebraic_cycle.
- Motive_(algebraic_geometry) wikiPageWikiLink Algebraic_geometry.
- Motive_(algebraic_geometry) wikiPageWikiLink Algebraic_group.
- Motive_(algebraic_geometry) wikiPageWikiLink Algebraic_variety.
- Motive_(algebraic_geometry) wikiPageWikiLink Birational_geometry.
- Motive_(algebraic_geometry) wikiPageWikiLink CW_complex.
- Motive_(algebraic_geometry) wikiPageWikiLink Categorical_adjunction.
- Motive_(algebraic_geometry) wikiPageWikiLink Category:Algebraic_geometry.
- Motive_(algebraic_geometry) wikiPageWikiLink Category:Homological_algebra.
- Motive_(algebraic_geometry) wikiPageWikiLink Category:Topological_methods_of_algebraic_geometry.
- Motive_(algebraic_geometry) wikiPageWikiLink Category_(mathematics).
- Motive_(algebraic_geometry) wikiPageWikiLink Category_theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Chow_ring.
- Motive_(algebraic_geometry) wikiPageWikiLink Cohomology.
- Motive_(algebraic_geometry) wikiPageWikiLink Complex_number.
- Motive_(algebraic_geometry) wikiPageWikiLink Correspondence_(mathematics).
- Motive_(algebraic_geometry) wikiPageWikiLink Crystalline_cohomology.
- Motive_(algebraic_geometry) wikiPageWikiLink Curve.
- Motive_(algebraic_geometry) wikiPageWikiLink Cyclotomic_character.
- Motive_(algebraic_geometry) wikiPageWikiLink De_Rham_cohomology.
- Motive_(algebraic_geometry) wikiPageWikiLink Derived_category.
- Motive_(algebraic_geometry) wikiPageWikiLink Equivalence_relation_on_cycles.
- Motive_(algebraic_geometry) wikiPageWikiLink Fields_Medal.
- Motive_(algebraic_geometry) wikiPageWikiLink Finite_field.
- Motive_(algebraic_geometry) wikiPageWikiLink French_language.
- Motive_(algebraic_geometry) wikiPageWikiLink Full_and_faithful_functors.
- Motive_(algebraic_geometry) wikiPageWikiLink Galois_group.
- Motive_(algebraic_geometry) wikiPageWikiLink Galois_module.
- Motive_(algebraic_geometry) wikiPageWikiLink Galois_theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Genus.
- Motive_(algebraic_geometry) wikiPageWikiLink Group_representation.
- Motive_(algebraic_geometry) wikiPageWikiLink Hodge_conjecture.
- Motive_(algebraic_geometry) wikiPageWikiLink Hodge_structure.
- Motive_(algebraic_geometry) wikiPageWikiLink Hodge_theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Homotopy_category_of_chain_complexes.
- Motive_(algebraic_geometry) wikiPageWikiLink If_and_only_if.
- Motive_(algebraic_geometry) wikiPageWikiLink Integer.
- Motive_(algebraic_geometry) wikiPageWikiLink Invariant_theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Karoubi_envelope.
- Motive_(algebraic_geometry) wikiPageWikiLink Lefschetz_motive.
- Motive_(algebraic_geometry) wikiPageWikiLink Lie_algebra.
- Motive_(algebraic_geometry) wikiPageWikiLink Linear_algebra.
- Motive_(algebraic_geometry) wikiPageWikiLink Local_zeta-function.
- Motive_(algebraic_geometry) wikiPageWikiLink Mayer–Vietoris_sequence.
- Motive_(algebraic_geometry) wikiPageWikiLink Milnor_conjecture.
- Motive_(algebraic_geometry) wikiPageWikiLink Monoidal_category.
- Motive_(algebraic_geometry) wikiPageWikiLink Morphism.
- Motive_(algebraic_geometry) wikiPageWikiLink Motivic_cohomology.
- Motive_(algebraic_geometry) wikiPageWikiLink Multiplicative_group.
- Motive_(algebraic_geometry) wikiPageWikiLink Mumford–Tate_group.
- Motive_(algebraic_geometry) wikiPageWikiLink Pierre_Deligne.
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- Motive_(algebraic_geometry) wikiPageWikiLink Representation_(mathematics).
- Motive_(algebraic_geometry) wikiPageWikiLink Rigid_category.
- Motive_(algebraic_geometry) wikiPageWikiLink Singular_homology.
- Motive_(algebraic_geometry) wikiPageWikiLink Standard_conjectures_on_algebraic_cycles.
- Motive_(algebraic_geometry) wikiPageWikiLink Tannaka–Krein_duality.
- Motive_(algebraic_geometry) wikiPageWikiLink Tannakian_category.
- Motive_(algebraic_geometry) wikiPageWikiLink Tate_conjecture.
- Motive_(algebraic_geometry) wikiPageWikiLink Triangulated_category.
- Motive_(algebraic_geometry) wikiPageWikiLink Vector_space.
- Motive_(algebraic_geometry) wikiPageWikiLink Vladimir_Voevodsky.
- Motive_(algebraic_geometry) wikiPageWikiLink Weil_cohomology_theory.
- Motive_(algebraic_geometry) wikiPageWikiLink Weil_conjectures.
- Motive_(algebraic_geometry) wikiPageWikiLink Étale_cohomology.
- Motive_(algebraic_geometry) wikiPageWikiLinkText "1-motives".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "Motive (algebraic geometry)".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "Motive".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "Motive_(algebraic_geometry)#Mixed_motives".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "category of motives".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "mixed motiv".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "motive (algebraic geometry)".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "motive".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "motives (algebraic geometry)".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "motives".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "motivic".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "pure motive".
- Motive_(algebraic_geometry) wikiPageWikiLinkText "pure motives".
- Motive_(algebraic_geometry) wikiPageUsesTemplate Template:Citation.
- Motive_(algebraic_geometry) wikiPageUsesTemplate Template:Citation_needed.
- Motive_(algebraic_geometry) wikiPageUsesTemplate Template:Other_uses.
- Motive_(algebraic_geometry) subject Category:Algebraic_geometry.
- Motive_(algebraic_geometry) subject Category:Homological_algebra.
- Motive_(algebraic_geometry) subject Category:Topological_methods_of_algebraic_geometry.