"Fourier\u2013Mukai transform"@en . . . . "Transform\u00E9e de Fourier-Mukai"@fr . "6847"^^ . . . . . . . . . . . . "8465724"^^ . . . . . "In algebraic geometry, a Fourier\u2013Mukai transform \u03A6K is a functor between derived categories of coherent sheaves D(X) \u2192 D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K \u2208 D(X\u00D7Y). Most natural functors, including basic ones like pushforwards and pullbacks, are of this type."@en . . . "In algebraic geometry, a Fourier\u2013Mukai transform \u03A6K is a functor between derived categories of coherent sheaves D(X) \u2192 D(Y) for schemes X and Y, which is, in a sense, an integral transform along a kernel object K \u2208 D(X\u00D7Y). 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 transform\u00E9e de Fourier-Mukai est un analogue en g\u00E9om\u00E9trie alg\u00E9brique de la transform\u00E9e de Fourier usuelle utilis\u00E9e en analyse. Elle a \u00E9t\u00E9 introduite par Shigeru Mukai."@fr . . . "1064793923"^^ . . . . . . . . . . . . . . . . . . . "La transform\u00E9e de Fourier-Mukai est un analogue en g\u00E9om\u00E9trie alg\u00E9brique de la transform\u00E9e de Fourier usuelle utilis\u00E9e en analyse. Elle a \u00E9t\u00E9 introduite par Shigeru Mukai."@fr . . . . .