Laumon introduced the local Fourier transform for ℓ-adic Galois representations of local fields, of equal characteristic p different from ℓ, as a powerful tool for studying the Fourier–Deligne transform of ℓ-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.
