On the $\ell$-adic Fourier transform and the determinant of the middle convolution

Abstract

We study the relation of the middle convolution to the $\ell$-adic Fourier transformation in the étale context. Using Katz' work and Laumon's theory of local Fourier transformations we obtain a detailed description of the local monodromy and the determinant of Katz' middle convolution functor $\MC_χ$ in the tame case. The theory of local $\epsilon$-constants then implies that the property of an étale sheaf of having an at most quadratic determinant is often preserved under $\MC_χ$ if $\chi$ is quadratic.

References in corpus (1)

• Hodge theory of the middle convolution