Local Fourier transform and epsilon factors

Abstract

AbstractLaumon introduced the local Fourier transform forℓ-adic Galois representations of local fields, of equal characteristicpdifferent fromℓ, as a powerful tool for studying the Fourier–Deligne transform ofℓ-adic sheaves over the affine line. In this article, we compute explicitly the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon’s formula relating the ε-factor to the determinant of the local Fourier transform under the same condition.