Homogeneous Fourier transform. (Transformation de Fourier homogène.) (French) Zbl 1088.11044

Laumon, Gérard

Bull. Soc. Math. Fr. 131, No. 4, 527-551 (2003).

Summary: In their proof of the Drinfeld-Langlands correspondence, E. Frenkel, D. Gaitsgory and K. Vilonen [J. Am. Math. Soc. 15, No. 2, 367–417 (2002; Zbl 1071.11039)] make use of a geometric Fourier transformation. Therefore, they work either with \(\ell \)-adic sheaves in characteristic \(p>0\), or with \(\mathcal D\)-modules in characteristic . Actually, they only need to consider the Fourier transforms of homogeneous sheaves for which one expects a geometric Fourier transformation over \(\mathbb Z\). In this note, we propose such a homogeneous geometric Fourier transformation. It extends the geometric Radon transformation which has been studied by J.-L. Brylinski [Géométrie et analyse microlocales, Astérisque 140/141, 3–134 (1986; Zbl 0624.32009)].

MSC:

11G09	Drinfel’d modules; higher-dimensional motives, etc.
11G45	Geometric class field theory
11R39	Langlands-Weil conjectures, nonabelian class field theory
11R58	Arithmetic theory of algebraic function fields
14D20	Algebraic moduli problems, moduli of vector bundles
14F05	Sheaves, derived categories of sheaves, etc. (MSC2010)

Keywords:

Fourier transformation; perverse sheaves; algebraic stacks