  In their proof of the Drinfeld-Langlands correspondence, Frenkel, Gaitsgory
and Vilonen make use of a geometric Fourier transformation. Therefore, they
work either with l-adic sheaves in characteristic p>0, or with D-modules in
characteristic 0. Actually, they only need to consider the Fourier transforms
of homogeneous sheaves for which one expects a uniform geometric construction
in any characteristic.
  In this note, we propose such a homogeneous geometric Fourier transformation.
It extends the geometric Radon transformation which has been studied by
Brylinski.

Algebraic Geometry