Katz-Radon transform of l-adic representations

TL;DR

This paper derives an explicit formula for the local Katz-Radon transform of l-adic Galois representations, linking it to additive convolution with a tame character, and addresses a question posed by Katz.

Contribution

It provides the first explicit formula for the local Katz-Radon transform in the l-adic setting, extending Arinkin's D-module results to Galois representations.

Findings

Explicit formula for the local Katz-Radon transform

Connection to additive convolution with tame characters

Answers a question posed by Katz

Abstract

We prove a simple explicit formula for the local Katz-Radon transform of an l-adic representation of the Galois group of the fraction field of a strictly henselian discrete valuation ring with positive residual characteristic, which can be defined as the local additive convolution with a fixed tame character. The formula is similar to one proved by D. Arinkin in the D-module setting, and answers a question posed by N. Katz.