We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two -adic sheaves on the torus 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.
Cite this article
Antonio Rojas-León, Explicit local multiplicative convolution of -adic sheaves. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1373–1386DOI 10.4171/RMI/1027