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
In mathematics, the derived category ''D''(''A'') of an abelian category ''A'' is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on ''A''. The construction pro ...
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
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
. It was used by
Gérard Laumon
Gérard Laumon (; born 1952) is a French mathematician, best known for his results in number theory, for which he was awarded the Clay Research Award.
Life and work
Laumon studied at the École Normale Supérieure and Paris-Sud 11 University, Or ...
to simplify Deligne's proof of the
Weil conjectures
In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory.
...
.
References
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Algebraic geometry
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