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- Coherent_duality abstract "In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry. This was re-expressed, with the advent of sheaf theory, in a way that made an analogy with Poincaré duality more apparent. Then according to a general principle, Grothendieck's relative point of view, the theory of Jean-Pierre Serre was extended to a proper morphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or complete variety) to a point. The resulting theory is now sometimes called Serre-Grothendieck-Verdier duality, and is a basic tool in algebraic geometry. A treatment of this theory, Residues and Duality (1966) by Robin Hartshorne, became an accessible reference. One concrete spin-off was the Grothendieck residue.To go beyond proper morphisms, as for the versions of Poincaré duality that are not for closed manifolds, requires some version of the compact support concept. This was addressed in SGA2 in terms of local cohomology, and Grothendieck local duality; and subsequently. The Greenlees-May duality, first formulated in 1976 by Ralf Strebel and in 1978 by Eben Matlis, is part of the continuing consideration of this area.".
- Coherent_duality wikiPageID "1815224".
- Coherent_duality wikiPageLength "10442".
- Coherent_duality wikiPageOutDegree "56".
- Coherent_duality wikiPageRevisionID "667493390".
- Coherent_duality wikiPageWikiLink Adjoint_functors.
- Coherent_duality wikiPageWikiLink Adjoint_linear_system.
- Coherent_duality wikiPageWikiLink Algebraic_geometry.
- Coherent_duality wikiPageWikiLink Amnon_Yekutieli.
- Coherent_duality wikiPageWikiLink Category:Duality_theories.
- Coherent_duality wikiPageWikiLink Category:Sheaf_theory.
- Coherent_duality wikiPageWikiLink Category:Topological_methods_of_algebraic_geometry.
- Coherent_duality wikiPageWikiLink Closed_manifold.
- Coherent_duality wikiPageWikiLink Coalgebra.
- Coherent_duality wikiPageWikiLink Cohen-Macaulay.
- Coherent_duality wikiPageWikiLink Cohen–Macaulay_ring.
- Coherent_duality wikiPageWikiLink Coherent_sheaf.
- Coherent_duality wikiPageWikiLink Coherent_sheaves.
- Coherent_duality wikiPageWikiLink Commutative_algebra.
- Coherent_duality wikiPageWikiLink Comonad.
- Coherent_duality wikiPageWikiLink Compact_support.
- Coherent_duality wikiPageWikiLink Complete_variety.
- Coherent_duality wikiPageWikiLink Complex_manifold.
- Coherent_duality wikiPageWikiLink Counit.
- Coherent_duality wikiPageWikiLink Derived_category.
- Coherent_duality wikiPageWikiLink Direct_image_with_compact_support.
- Coherent_duality wikiPageWikiLink Dualizing_sheaf.
- Coherent_duality wikiPageWikiLink Eben_Matlis.
- Coherent_duality wikiPageWikiLink Exact_functor.
- Coherent_duality wikiPageWikiLink Exceptional_inverse_image_functor.
- Coherent_duality wikiPageWikiLink Ext_functor_of_sheaves.
- Coherent_duality wikiPageWikiLink Glossary_of_algebraic_geometry.
- Coherent_duality wikiPageWikiLink Gorenstein_ring.
- Coherent_duality wikiPageWikiLink Greenlees-May_duality.
- Coherent_duality wikiPageWikiLink Grothendieck_local_duality.
- Coherent_duality wikiPageWikiLink Grothendieck_residue.
- Coherent_duality wikiPageWikiLink Grothendieck_residue_symbol.
- Coherent_duality wikiPageWikiLink Grothendiecks_relative_point_of_view.
- Coherent_duality wikiPageWikiLink Hochschild_cohomology.
- Coherent_duality wikiPageWikiLink Hochschild_homology.
- Coherent_duality wikiPageWikiLink Homological_algebra.
- Coherent_duality wikiPageWikiLink Invertible_sheaf.
- Coherent_duality wikiPageWikiLink Jean-Pierre_Serre.
- Coherent_duality wikiPageWikiLink Joseph_Lipman.
- Coherent_duality wikiPageWikiLink Journal_of_the_American_Mathematical_Society.
- Coherent_duality wikiPageWikiLink Krull_dimension.
- Coherent_duality wikiPageWikiLink Line_bundle.
- Coherent_duality wikiPageWikiLink Linear_system_of_divisors.
- Coherent_duality wikiPageWikiLink Local_cohomology.
- Coherent_duality wikiPageWikiLink Localization_of_a_ring.
- Coherent_duality wikiPageWikiLink Monad_(category_theory).
- Coherent_duality wikiPageWikiLink Natural_transformation.
- Coherent_duality wikiPageWikiLink Non-singular.
- Coherent_duality wikiPageWikiLink Oxford_University_Press.
- Coherent_duality wikiPageWikiLink Poincaré_duality.
- Coherent_duality wikiPageWikiLink Projective_variety.
- Coherent_duality wikiPageWikiLink Proper_morphism.
- Coherent_duality wikiPageWikiLink Quasi-coherent_sheaves.
- Coherent_duality wikiPageWikiLink Ralf_Strebel.
- Coherent_duality wikiPageWikiLink Right_adjoint.
- Coherent_duality wikiPageWikiLink Robin_Hartshorne.
- Coherent_duality wikiPageWikiLink SGA2.
- Coherent_duality wikiPageWikiLink Serre_duality.
- Coherent_duality wikiPageWikiLink Sheaf_(mathematics).
- Coherent_duality wikiPageWikiLink Sheaf_cohomology.
- Coherent_duality wikiPageWikiLink Sheaf_theory.
- Coherent_duality wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Coherent_duality wikiPageWikiLink Springer-Verlag.
- Coherent_duality wikiPageWikiLink Springer_Science+Business_Media.
- Coherent_duality wikiPageWikiLink Support_(mathematics).
- Coherent_duality wikiPageWikiLink Séminaire_de_Géométrie_Algébrique_du_Bois_Marie.
- Coherent_duality wikiPageWikiLink Verdier_duality.
- Coherent_duality wikiPageWikiLinkText "Coherent duality".
- Coherent_duality wikiPageWikiLinkText "Grothendieck duality".
- Coherent_duality wikiPageWikiLinkText "coherent duality".
- Coherent_duality hasPhotoCollection Coherent_duality.
- Coherent_duality wikiPageUsesTemplate Template:Citation.
- Coherent_duality wikiPageUsesTemplate Template:Images_of_sheaves.
- Coherent_duality subject Category:Duality_theories.
- Coherent_duality subject Category:Sheaf_theory.
- Coherent_duality subject Category:Topological_methods_of_algebraic_geometry.
- Coherent_duality hypernym Part.
- Coherent_duality type Method.
- Coherent_duality type Theory.
- Coherent_duality comment "In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.The historical roots of the theory lie in the idea of the adjoint linear system of a linear system of divisors in classical algebraic geometry.".
- Coherent_duality label "Coherent duality".
- Coherent_duality sameAs m.05z44k.
- Coherent_duality sameAs Q5141352.
- Coherent_duality sameAs Q5141352.
- Coherent_duality wasDerivedFrom Coherent_duality?oldid=667493390.
- Coherent_duality isPrimaryTopicOf Coherent_duality.