Galois structure of S-units

TL;DR

This paper investigates the Galois module structure of S-units in a number field extension, providing a method to construct a G-module that relates to the S-unit module and free modules.

Contribution

It introduces a construction of a G-module from known data that is stably isomorphic to the S-unit module plus a free module, advancing understanding of Galois module structures.

Findings

Constructs a G-module M from data determining the stable isomorphism class of E.

Shows M is stably isomorphic to E plus a free G-module.

Provides a method to analyze the Galois module structure of S-units.

Abstract

Let K/k be a finite Galois extension of number fields with Galois group G, S a large set of primes of K, and E the G-module of S-units of K. Previous work has determined the data which is necessary to determine the stable isomorphism class of E. This paper explains how to build a G-module M from this data which has the property that M is stably isomorphic to the direct sum of E and some free G-module F.