Monodromy at Infinity and Fourier Transform

Abstract

Let $f:U\to \mathbf{C}$ be a regular function on a smooth quasi-projective variety $U$. We compute the limit mixed Hodge structure (when $t\to \infty$) of the cohomology of the fibers $f=t$ in terms of the Fourier transform of the Gauss–Manin system associated to $f$.