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

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)

Citations:

Zbl 1071.11039; Zbl 0624.32009
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