Calculation of ℓ-adic local Fourier transformations

Abstract

We calculate the local Fourier transformations for a class of \({\overline{\mathbb Q}_\ell}\)-sheaves. In particular, we verify a conjecture of Laumon and Malgrange [18, 2.6.3]. As an application, we calculate the local monodromy of ℓ-adic hypergeometric sheaves introduced by Katz [15]. We also discuss the characteristic p analogue of the Turrittin-Levelt Theorem for D-modules.