Hypergeometric period for a tame polynomial

We analyze the Gauss-Manin system of differential equations (and its Fourier transform) attached to regular functions satisfying a tameness assumption on a smooth affine variety over C (e.g. tame polynomials on Cn+1). We give a solution to the Birkhoff problem for this system and prove Hedge-type results analogous to those existing for germs of isolated hypersurface singularities. We deduce a formula for the determinant of the "Aomoto complex". (C) Academie des Sciences/Elsevier, Paris.