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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  • 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)
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  • 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)
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  • Fourier–Mukai transform (en)
  • Transformée de Fourier-Mukai (fr)
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