About: Fourier–Mukai transform

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In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type.

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rdfs:label	Fourier–Mukai transform (en) Transformée de Fourier-Mukai (fr)
rdfs:comment	La transformée de Fourier-Mukai est un analogue en géométrie algébrique de la transformée de Fourier usuelle utilisée en analyse. Elle a été introduite par Shigeru Mukai. (fr) In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type. (en)
dct:subject	Abelian varieties
Wikipage page ID	8465724 (xsd:integer)
Wikipage revision ID	1064793923 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector space Derived category Derived functor Derived noncommutative algebraic geometry Integral transform Inverse image functor Pontryagin product Equivalence of categories Standard conjectures on algebraic cycles Functor Dual abelian variety Adjoint functor Algebraic geometry Ample line bundle Fourier transform Direct image functor T-duality Projective variety Tensor product Tensor product of modules Abelian variety Abelian varieties Coherent sheaf Distribution (mathematics) Canonical bundle Scheme (mathematics) Smooth scheme Dual vector space Chow motive Poincaré bundle
Link from a Wikipage to an external page	http://projecteuclid.org/euclid.nmj/1118786312
sameAs	Fourier–Mukai transform Fourier–Mukai transform Fourier–Mukai transform Fourier–Mukai transform
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal dbt:Harvtxt dbt:Reflist dbt:Harvs
has abstract	In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K ∈ D(X×Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type. These kinds of functors were introduced by Mukai in order to prove an equivalence between the derived categories of coherent sheaves on an abelian variety and its dual. That equivalence is analogous to the classical Fourier transform that gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual. (en) La transformée de Fourier-Mukai est un analogue en géométrie algébrique de la transformée de Fourier usuelle utilisée en analyse. Elle a été introduite par Shigeru Mukai. (fr)
gold:hypernym	Isomorphism
prov:wasDerivedFrom	wikipedia-en:Fourier–Mukai_transform?oldid=1064793923&ns=0
page length (characters) of wiki page	6847 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Fourier–Mukai_transform
is Link from a Wikipage to another Wikipage of	Derived category Derived noncommutative algebraic geometry Tom Bridgeland Triangulated category Fourier transform Shigeru Mukai Fourier-Mukai transform List of things named after Joseph Fourier Mukai-Fourier transform Mukai transform Mukai vector Mukai–Fourier transform
is Wikipage redirect of	Fourier-Mukai transform Mukai-Fourier transform Mukai transform Mukai vector Mukai–Fourier transform
is foaf:primaryTopic of	wikipedia-en:Fourier–Mukai_transform

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