Nothing Special   »   [go: up one dir, main page]

About: Cotangent complex

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If is a morphism of geometric or algebraic objects, the corresponding cotangent complex can be thought of as a universal "linearization" of it, which serves to control the deformation theory of . It is constructed as an object in a certain derived category of sheaves on using the methods of homotopical algebra.

thumbnail
Property Value
dbo:abstract
  • In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If is a morphism of geometric or algebraic objects, the corresponding cotangent complex can be thought of as a universal "linearization" of it, which serves to control the deformation theory of . It is constructed as an object in a certain derived category of sheaves on using the methods of homotopical algebra. Restricted versions of cotangent complexes were first defined in various cases by a number of authors in the early 1960s. In the late 1960s, Michel André and Daniel Quillen independently came up with the correct definition for a morphism of commutative rings, using simplicial methods to make precise the idea of the cotangent complex as given by taking the (non-abelian) left derived functor of Kähler differentials. Luc Illusie then globalized this definition to the general situation of a morphism of ringed topoi, thereby incorporating morphisms of ringed spaces, schemes, and algebraic spaces into the theory. (en)
dbo:thumbnail
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 17346860 (xsd:integer)
dbo:wikiPageLength
  • 30025 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1122789313 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdfs:comment
  • In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If is a morphism of geometric or algebraic objects, the corresponding cotangent complex can be thought of as a universal "linearization" of it, which serves to control the deformation theory of . It is constructed as an object in a certain derived category of sheaves on using the methods of homotopical algebra. (en)
rdfs:label
  • Cotangent complex (en)
owl:sameAs
prov:wasDerivedFrom
foaf:depiction
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License