Search

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.

We give some estimates for multiplicative character sums on quasiprojective varieties over flnite flelds depending on the severity of the singularities of the variety at inflnity. We also remove the hypothesis of non-divisibility by the characteristic of the base fleld in the known estimates for the non-singular case.