Transformation de Fourier generalisee

Details Transformation de Fourier generalisee Transformation de Fourier generalisee

1996-03-05

arxiv.org/abs/alg-geom/9603004v1

Mathematics

Algebraic Geometry

This is a revised version of an IHES preprint (Transformation de Fourier geometrique, IHES/85/M/52) 47 pages, no figure. Plain

Scientific paper

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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