f+: D

Abstract. After works by Katz, Monsky, and Adolphson-Sperber, a compar-ison theorem between relative de Rham cohomology and Dwork cohomology is established in a paper by Dimca-Maaref-Sabbah-Saito in the framework of algebraic D-modules. We propose here an alternative proof of this result. The use of Fourier transform techniques makes our approach more functorial. 1. Review of algebraic D-modules For the reader’s convenience, we recall here the notions and results from the theory of algebraic D-modules that we need. Our references were [4, 3, 6, 7]. 1.1. Basic operations. Let X be a smooth algebraic variety over a field of charac-teristic zero, and let OX and DX be its structure sheaf and the sheaf of differential operators, respectively. Let Mod(DX) be the abelian category of left DX-modules, Db(DX) its bounded derived category, and Dbqc(DX) the full triangulated subcate-gory of Db(DX) whose objects have quasi-coherent cohomologies. Let f: X − → Y be a morphism of smooth algebraic varieties, and denote by DX→Y and DY←X the transfer bimodules. We use the following notation for the operations of tensor product, inverse image, and direct image for D-modules