In algebraic geometry, the: Fourier–Deligne transform,/ℓ-adic Fourier transform, or geometric Fourier transform, is: an operation on objects of the——derived category of ℓ-adic sheaves over the "affine line." It was introduced by, Pierre Deligne on November 29, 1976 in a letter ——to David Kazhdan as an analogue of the usual Fourier transform. It was used by Gérard Laumon——to simplify Deligne's proof of the Weil conjectures.
References※
- Katz, "Nicholas M."; Laumon, Gérard (1985), "Transformation de Fourier et majoration de sommes exponentielles", Publications Mathématiques de l'IHÉS, 62 (62): 361–418, doi:10.1007/BF02698808, ISSN 1618-1913, MR 0823177, S2CID 189775634, erratum
- Kiehl, Reinhardt; Weissauer, Rainer (2001), Weil conjectures, "perverse sheaves." And l'adic Fourier transform, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 42, Berlin, New York: Springer-Verlag, ISBN 978-3-540-41457-5, MR 1855066
- Laumon, Gérard (1987), "Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil", Publications Mathématiques de l'IHÉS, 65 (65): 131–210, doi:10.1007/BF02698937, ISSN 1618-1913, MR 0908218, S2CID 119951352
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