Quelques calculs de sommes de Gauss

TL;DR

This paper explores how Galois actions on local constants of Galois representations reveal their arithmetic properties, including bounds on their order and effects of Adams operations.

Contribution

It provides new insights into the arithmetic nature of local constants through Galois actions and their relation to Adams operations.

Findings

Galois action gives bounds on the order of local constants.

Galois action informs about the effect of Adams operations.

Local constants' arithmetic properties are elucidated.

Abstract

We observe that the Galois action on local constants associated to Galois representations of a local field yields information on their arithmetic nature, for example provides an upper bound to their order when they are roots of unity. It also yields information on the effect of Adams operations on these constants.