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Six operations

In mathematics, Grothendieck's six operations, named after Alexander Grothendieck, is a formalism in homological algebra, also known as the six-functor formalism. It originally sprang from the relations in étale cohomology that arise from a morphism of schemes f : X → Y. The basic insight was that many of the elementary facts relating cohomology on X and…

Products, Six operations in étale cohomology & The operations

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The operations

Six operations in étale cohomology

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Six operations

Nodes36
Edges35
Triples52
Avg. degree1.94
Density0.055556
Components1

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Six operations

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related to References · 31
Six operations → Artin, Ayoub, Cisinski, Cours, Denis-Charles, DX-modules, Déglise, Finite, Frédéric, Grothendieck, Hermann, ISBN, Joseph, Laszlo, Le, Les, Martin, Mathematics, Mebkhout, Olsson
related to Six operations in étale cohomology · 17
Six operations → Artin, Finally, Furthermore, Grothendieck, Hom, If, III, In, In SGA, Let, Lf, Rf, RHom, Specifically, Suppose, Tate, The
related to External links · 1
Six operations → Grothendieck's

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Important terminology

six displaystyle operations functors sheaves derived category morphism grothendieck also cohomology adjoint formalism schemes categories image tensor product functor many

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SubjectPredicateObjectConfidenceSrc
D-modules on algebraic varietiesinstance ofThe six operations formalism has since been shown to apply to contexts0.80text
sheaves on locally compact topological spacesinstance ofThe six operations formalism has since been shown to apply to contexts0.80text
and motivesinstance ofThe six operations formalism has since been shown to apply to contexts0.80text
Six operationsrelated to External linksGrothendieck's0.60section
Six operationsrelated to ReferencesLaszlo0.60section
Six operationsrelated to ReferencesYves0.60section
Six operationsrelated to ReferencesOlsson0.60section
Six operationsrelated to ReferencesMartin0.60section
Six operationsrelated to ReferencesThe0.60section
Six operationsrelated to ReferencesArtin0.60section
Six operationsrelated to ReferencesFinite0.60section
Six operationsrelated to ReferencesAyoub0.60section

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