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)].


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)
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