Fourier transform for D-algebras, I

Abstract

An analogue of the Fourier transform is developed for D-algebras. G. Laumon's equivalence between the derived category of $\mathscr {D}$-modules on an abelian variety and the derived category of $\mathscr {O}$-modules on the universal extension of the dual variety is seen as a degenerate case of a duality for twisted differential operators (tdo's) with respect to which the dual of a generic tdo is again a tdo.