an:02096366
Zbl 1088.11044
Laumon, G??rard
Homogeneous Fourier transform
FR
Bull. Soc. Math. Fr. 131, No. 4, 527-551 (2003).
00101247
2003
j
11G09 11G45 11R39 11R58 14D20 14F05
Fourier transformation; perverse sheaves; algebraic stacks
Summary: In their proof of the Drinfeld-Langlands correspondence, \textit{E. Frenkel, D. Gaitsgory} and \textit{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 \textit{J.-L. Brylinski} [G??om??trie et analyse microlocales, Ast??risque 140/141, 3--134 (1986; Zbl 0624.32009)].
Zbl 1071.11039; Zbl 0624.32009