La transformation de Fourier pour les ūĚíü-modules
Annales de l'Institut Fourier, Volume 50 (2000) no. 6, pp. 1891-1944.

Let ‚ĄĪ be the Fourier transform for ūĚíü-Modules over ‚Ąā n , let ‚ĄĪ + be the Fourier transform for sheaves defined by Brylinsky-Malgrange-Verdier, and let ūĚíģol be the ‚Äúsolutions‚ÄĚ functor. We prove that for any ūĚíü-Module ‚Ą≥ 1-specialisable at infinity, there is an isomorphism ūĚíģol(‚ĄĪ‚Ą≥)‚Č°‚ĄĪ + ūĚíģol(‚Ą≥). This result was conjectured in 1988 by B. Malgrange, who proved it for the particular case of modules of finite type over the Weyl algebra.

Sur ‚Ąā n vu comme vari√©t√© alg√©brique, soient ‚ĄĪ la transformation de Fourier pour les ūĚíü-modules, ‚ĄĪ + la transformation de Fourier faisceautique de Brylinsky-Malgrange-Verdier, et ūĚíģol le foncteur ‚Äúsolutions‚ÄĚ. On prouve alors que pour tout ūĚíü-module 1-sp√©cialisable √† l‚Äôinfini ‚Ą≥, on a un isomorphisme ūĚíģol(‚ĄĪ‚Ą≥)‚Č°‚ĄĪ + ūĚíģol(‚Ą≥). Le r√©sultat a √©t√© conjectur√© en 1988 par B. Malgrange, qui l‚Äôa prouv√© pour ‚Ą≥ module de type fini sur l‚Äôalg√®bre de Weyl.

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     title = {La transformation de {Fourier} pour les ${\mathcal {D}}$-modules},
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Daia, Liviu. La transformation de Fourier pour les ${\mathcal {D}}$-modules. Annales de l'Institut Fourier, Volume 50 (2000) no. 6, pp. 1891-1944. doi : 10.5802/aif.1810. http://www.numdam.org/articles/10.5802/aif.1810/

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