Local Fourier transform and epsilon factors

Abstract

Laumon introduced the local Fourier transform for $\ell$-adic Galois representations of local fields, of equal characteristic $p$ different from $\ell$, as a powerful tool to study the Fourier-Deligne transform of $\ell$-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 epsilon factor to the determinant of the local Fourier transform under the same condition.

Cited by in corpus (10)

• Local Galois representations of Swan conductor one
• A microlocal approach to the enhanced Fourier-Sato transform in dimension one
• Product formula for p-adic epsilon factors
• Geometric local epsilon factors
• Gauss sums and Van der Geer--Van der Vlugt curves
• Calculation of l-adic local Fourier transformations
• L-functions of symmetric powers of the generalized Airy family of exponential sums
• Ramification and nearby cycles for l-adic sheaves on relative curves
• L-functions of symmetric powers of the generalized Airy family of exponential sums: ell-adic and p-adic methods
• Galois-module theory for wildly ramified covers of curves over finite fields