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In 1996, Rothstein and Laumon simultaneously constructed a Fourier-Mukaitransform for D-modules over a locally noetherian base of characteristic 0.This functor induces an equivalence of categories between quasi-coherentsheaves of D-modules over an abelian variety A and quasicoherent sheaves ofO-modules over its universal vectorial extension A. In this article, we definea Fourier-Mukai transform for D-modules on an abelian formal scheme A/S = Spf(V), where V is a discrete valuation ring, and we discuss the extension of theclassical results of Fourier-Mukai transform to this arithmetic case.

Fourier-Muka\"i transform for $\mathcal{D}^{(0)}$-modules over formal abelian schemes