About: Coherent duality

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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.

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rdfs:label	Coherent duality (en)
rdfs: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. (en)
dcterms:subject	Duality theories Topological methods of algebraic geometry Sheaf theory
Wikipage page ID	1815224 (xsd:integer)
Wikipage revision ID	1112014788 (xsd:integer)
Link from a Wikipage to another Wikipage	Robin Hartshorne Non-singular Joseph Lipman Derived category Invertible sheaf Comonad Compact support Counit Natural transformation Duality theories Topological methods of algebraic geometry Luchezar L. Avramov Closed manifold Commutative algebra Complete variety Complex manifold Krull dimension Dualizing sheaf Coherent sheaves Line bundle Linear system of divisors Local cohomology Poincaré duality Algebraic geometry Amnon Yekutieli Oxford University Press Direct image with compact support Gorenstein ring Journal of the American Mathematical Society Projective variety Proper morphism Jean-Pierre Serre Sheaf theory Eben Matlis Homological algebra Grothendieck's relative point of view Grothendieck local duality Field of fractions Exact functor Exceptional inverse image functor Verdier duality Sheaf cohomology Glossary of algebraic geometry Hochschild cohomology Right adjoint Springer-Verlag SGA2 Quasi-coherent sheaves Cohen–Macaulay Sheaf theory dbr:Adjoint_linear_system dbr:Ext_functor_of_sheaves dbr:Greenlees–May_duality dbr:Grothendieck_residue dbr:Grothendieck_residue_symbol dbr:Ralf_Strebel
Link from a Wikipage to an external page	https://www.ams.org/journals/tran/1983-275-02/S0002-9947-1983-0682716-X/S0002-9947-1983-0682716-X.pdf
sameAs	Coherent duality Coherent duality Coherent duality Coherent duality
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Images_of_sheaves
has 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 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 a reference. One concrete spin-off was the . 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 , first formulated in 1976 by and in 1978 by Eben Matlis, is part of the continuing consideration of this area. (en)
prov:wasDerivedFrom	wikipedia-en:Coherent_duality?oldid=1112014788&ns=0
page length (characters) of wiki page	12847 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Coherent_duality
is rdfs:seeAlso of	Direct image functor
is Link from a Wikipage to another Wikipage of	List of algebraic geometry topics List of dualities Derived category Timeline of category theory and related mathematics Glossary of algebraic geometry Luchezar L. Avramov Triangulated category Dualizing sheaf Alexander Grothendieck Duality (mathematics) Brown's representability theorem Fondements de la Géometrie Algébrique

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