Calculation of l-adic local Fourier transformations

Abstract

We calculate the local Fourier transformations for a class of ${\bar{\mathbb{Q}}}_{\ell }$-sheaves. In particular, we verify a conjecture of Laumon and Malgrange. As an application, we calculate the local monodromy of $\ell$-adic hypergeometric sheaves introduced by Katz. We also discuss the characteristic $p$ analogue of the Turrittin-Levelt Theorem for $D$-modules. The method used in this paper can be used to show a conjecture of Ramero which states that the Fourier transformation of an analytic sheaf with meromorphic ramification still has meromorphic ramification.

61 pages. Final version. To appear in Manuscripta Mathematica

References in corpus (1)

• Local Fourier transform and epsilon factors

Cited by in corpus (1)

• L-functions of symmetric powers of the generalized Airy family of exponential sums