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arxiv: alg-geom/9603004 · v1 · submitted 1996-03-05 · alg-geom · math.AG

Transformation de Fourier generalisee

Gerard Laumon This is my paper
classification alg-geom math.AG
keywords transformationabeliand-modulesgeometriccategoryconstructderivedequivalence
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In this paper I construct a geometric transformation for generalized 1-motives which extends the Fourier-Mukai transformation for O-Modules on abelian varieties, the geometric Fourier transformation for D-Modules on vector spaces and the geometric Mellin transformation for D-Modules on tori. In particular, I construct an equivalence of triangulated categories between the derived category of quasi-coherent D-Modules on an abelian variety and the derived category of quasi-coherent O-Modules on the universal extension of the dual abelian variety. This equivalence has also been obtained by Mitchell Rothstein.

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