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In algebraic geometry, the Fourier–Deligne transform, or ℓ-adic Fourier transform, or geometric Fourier transform, is an operation on objects of the derived category of -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.


  • Katz, Nicholas M.; Laumon, Gérard (1985), "Transformation de Fourier et majoration de sommes exponentielles", Publications Mathématiques de l'IHÉS (62): 361–418, ISSN 1618-1913, MR 0823177, 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, 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): 131–210, ISSN 1618-1913, MR 0908218