分野別セミナー

Laumon introduced the local Fourier transform for l-adic Galois representations of locals fields, of equal characteristic p different from l, as a powerful tool to study the Fourier-Deligne transform of l-adic sheaves over the affine line. He used it to prove that the constant of the functional equation of the L-function associated to an l-adic representation of a function field is a product of local constants,
also known as epsilon factors. Along the way, he gave a cohomological interpretation of epsilon factors
in terms of the determinant of the local Fourier transform.
In a joint work with T. Saito, we compute the local Fourier transform of monomial representations satisfying a certain ramification condition, and deduce Laumon's formula for epsilon factors under the same condition. Our approach, inspired by our ramification theory, is local and geometric, while Laumon'approach is global, combining arithmetic and geometric arguments.