2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150120In 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.This is a revised version of an IHES preprint (Transformation de Fourier geometrique, IHES/85/M/52) 47 pages, no figure. PlainTeXAlgebraic Geometry14F05 (Primary) 14K05 (Secondary)text