Explicit local multiplicative convolution of $\ell$-adic sheaves

Abstract

We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two $\ell$-adic sheaves on the torus ${\mathbb{G}}_m$ over the algebraic closure of a finite field in terms of the local monodromies of the factors. As a particular case, we recover Fu's formulas for the local Fourier transform.