Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Derived_category> ?p ?o }
- Derived_category abstract "In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology. The definitions lead to a significant simplification of formulas otherwise described (not completely faithfully) by complicated spectral sequences.The development of the derived category, by Alexander Grothendieck and his student Jean-Louis Verdier shortly after 1960, now appears as one terminal point in the explosive development of homological algebra in the 1950s, a decade in which it had made remarkable strides. The basic theory of Verdier was written down in his dissertation, published finally in 1996 in Astérisque (a summary much earlier appeared in SGA 4½). The axiomatics required an innovation, the concept of triangulated category, and the construction is based on localization of a category, a generalization of localization of a ring. The original impulse to develop the "derived" formalism came from the need to find a suitable formulation of Grothendieck's coherent duality theory. Derived categories have since become indispensable also outside of algebraic geometry, for example in the formulation of the theory of D-modules and microlocal analysis. Recently the derived categories have also become important in areas nearer to physics, such as D-branes and mirror symmetry.".
- Derived_category wikiPageExternalLink DerivedCats.pdf.
- Derived_category wikiPageExternalLink fitem?id=ASENS_1994_4_27_1_63_0.
- Derived_category wikiPageExternalLink fitem?id=CM_1988__65_2_121_0.
- Derived_category wikiPageExternalLink dcu.ps.
- Derived_category wikiPageID "985897".
- Derived_category wikiPageLength "17285".
- Derived_category wikiPageOutDegree "87".
- Derived_category wikiPageRevisionID "649202161".
- Derived_category wikiPageWikiLink Abelian_category.
- Derived_category wikiPageWikiLink Alexander_Grothendieck.
- Derived_category wikiPageWikiLink Algebraic_geometry.
- Derived_category wikiPageWikiLink Category:Category-theoretic_categories.
- Derived_category wikiPageWikiLink Category:Homological_algebra.
- Derived_category wikiPageWikiLink Category_(mathematics).
- Derived_category wikiPageWikiLink Chain_complex.
- Derived_category wikiPageWikiLink Chain_complexes.
- Derived_category wikiPageWikiLink Chain_homotopy.
- Derived_category wikiPageWikiLink Class_(set_theory).
- Derived_category wikiPageWikiLink Cohen-Macaulay_ring.
- Derived_category wikiPageWikiLink Cohen–Macaulay_ring.
- Derived_category wikiPageWikiLink Coherent_duality.
- Derived_category wikiPageWikiLink Coherent_sheaf.
- Derived_category wikiPageWikiLink Cohomology.
- Derived_category wikiPageWikiLink Cokernel.
- Derived_category wikiPageWikiLink D-brane.
- Derived_category wikiPageWikiLink D-branes.
- Derived_category wikiPageWikiLink D-module.
- Derived_category wikiPageWikiLink Derived_functor.
- Derived_category wikiPageWikiLink Derived_functors.
- Derived_category wikiPageWikiLink Direct_image_functor.
- Derived_category wikiPageWikiLink Epimorphism.
- Derived_category wikiPageWikiLink Equivalence_of_categories.
- Derived_category wikiPageWikiLink Exact_category.
- Derived_category wikiPageWikiLink Exact_sequence.
- Derived_category wikiPageWikiLink Ext_functor.
- Derived_category wikiPageWikiLink Ext_functors.
- Derived_category wikiPageWikiLink Functor.
- Derived_category wikiPageWikiLink Global_section_functor.
- Derived_category wikiPageWikiLink Global_sections_functor.
- Derived_category wikiPageWikiLink Grothendieck_category.
- Derived_category wikiPageWikiLink Grothendieck_spectral_sequence.
- Derived_category wikiPageWikiLink Grothendiecks_Sxc3xa9minaire_de_gxc3xa9omxc3xa9trie_algxc3xa9brique.
- Derived_category wikiPageWikiLink Group_cohomology.
- Derived_category wikiPageWikiLink Higher_direct_image_functor.
- Derived_category wikiPageWikiLink Homological_algebra.
- Derived_category wikiPageWikiLink Homology_(mathematics).
- Derived_category wikiPageWikiLink Homotopy.
- Derived_category wikiPageWikiLink Homotopy_category_of_chain_complexes.
- Derived_category wikiPageWikiLink Homotopy_theory.
- Derived_category wikiPageWikiLink Hyperhomology.
- Derived_category wikiPageWikiLink Injective_object.
- Derived_category wikiPageWikiLink Injective_resolution.
- Derived_category wikiPageWikiLink Isomorphism.
- Derived_category wikiPageWikiLink Jean-Louis_Verdier.
- Derived_category wikiPageWikiLink Kan_extension.
- Derived_category wikiPageWikiLink Localization_of_a_category.
- Derived_category wikiPageWikiLink Localization_of_a_ring.
- Derived_category wikiPageWikiLink Mapping_cone_(homological_algebra).
- Derived_category wikiPageWikiLink Mathematics.
- Derived_category wikiPageWikiLink Microlocal_analysis.
- Derived_category wikiPageWikiLink Mikio_Sato.
- Derived_category wikiPageWikiLink Mirror_symmetry_(string_theory).
- Derived_category wikiPageWikiLink Model_category.
- Derived_category wikiPageWikiLink Module_(mathematics).
- Derived_category wikiPageWikiLink Monomorphism.
- Derived_category wikiPageWikiLink Non-singular.
- Derived_category wikiPageWikiLink Object_(category_theory).
- Derived_category wikiPageWikiLink Projective_object.
- Derived_category wikiPageWikiLink Quasi-isomorphism.
- Derived_category wikiPageWikiLink Resolution_(algebra).
- Derived_category wikiPageWikiLink Riemann-Hilbert_correspondence.
- Derived_category wikiPageWikiLink Riemann–Hilbert_correspondence.
- Derived_category wikiPageWikiLink Ring_(mathematics).
- Derived_category wikiPageWikiLink Scheme_(mathematics).
- Derived_category wikiPageWikiLink Serre_duality.
- Derived_category wikiPageWikiLink Set_(mathematics).
- Derived_category wikiPageWikiLink Sheaf_(mathematics).
- Derived_category wikiPageWikiLink Sheaf_cohomology.
- Derived_category wikiPageWikiLink Singular_point_of_an_algebraic_variety.
- Derived_category wikiPageWikiLink Société_Mathématique_de_France.
- Derived_category wikiPageWikiLink Société_mathématique_de_France.
- Derived_category wikiPageWikiLink Spectral_sequence.
- Derived_category wikiPageWikiLink Spectrum_(homotopy_theory).
- Derived_category wikiPageWikiLink Spectrum_(topology).
- Derived_category wikiPageWikiLink Springer-Verlag.
- Derived_category wikiPageWikiLink Springer_Science+Business_Media.
- Derived_category wikiPageWikiLink Subcategory.
- Derived_category wikiPageWikiLink Séminaire_de_Géométrie_Algébrique_du_Bois_Marie.
- Derived_category wikiPageWikiLink Tensor_product.
- Derived_category wikiPageWikiLink Topological_space.
- Derived_category wikiPageWikiLink Triangulated_category.
- Derived_category wikiPageWikiLink Étale_cohomology.
- Derived_category wikiPageWikiLinkText "Derived categories".
- Derived_category wikiPageWikiLinkText "Derived category".
- Derived_category wikiPageWikiLinkText "derived categories".
- Derived_category wikiPageWikiLinkText "derived category".
- Derived_category wikiPageWikiLinkText "derived".
- Derived_category first "M.G.M. van".
- Derived_category hasPhotoCollection Derived_category.