Explicit local multiplicative convolution of l-adic sheaves

TL;DR

This paper provides explicit formulas for local multiplicative convolution functors that relate the local monodromies of convoluted l-adic sheaves on the torus to those of the original sheaves, enhancing understanding of their monodromic behavior.

Contribution

It introduces explicit formulas for local multiplicative convolution functors for l-adic sheaves on the torus, connecting local monodromies of convolutions to those of individual sheaves.

Findings

Explicit formulas for local monodromies of convoluted sheaves

Connection between local monodromies of factors and convolution

Enhanced understanding of l-adic sheaf convolutions on the torus

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.