Fourier–Deligne transform

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 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

{{Citation | last1=Katz | first1=Nicholas M. | authorlink1=Nick Katz | last2=Laumon | first2=Gérard | authorlink2=Gérard Laumon | title=Transformation de Fourier et majoration de sommes exponentielles | url=http://www.numdam.org/item?id=PMIHES_1985__62__145_0 | mr=823177 |id= [http://www.numdam.org/item?id=PMIHES_1989__69__233_0 erratum] | year=1985 | journal=Publications Mathématiques de l'IHÉS | volume=62 | issn=1618-1913 | issue=62 | pages=361–418| doi=10.1007/BF02698808 | s2cid=189775634 }}
{{Citation | authorlink1=Reinhardt Kiehl|last1=Kiehl | first1=Reinhardt | last2=Weissauer | first2=Rainer | title=Weil conjectures, perverse sheaves and l'adic Fourier transform | publisher=Springer-Verlag | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics | isbn=978-3-540-41457-5 | mr=1855066 | year=2001 | volume=42}}
{{Citation | last1=Laumon | first1=Gérard | title=Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil | url=http://www.numdam.org/item?id=PMIHES_1987__65__131_0 | mr=908218 | year=1987 | journal=Publications Mathématiques de l'IHÉS | volume=65 | issn=1618-1913 | issue=65 | pages=131–210| doi=10.1007/BF02698937 | s2cid=119951352 }}