This book is the result of a short course on the Galois structure of $S$-units that was given at The Fields Institute in the fall of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behavior of Artin $L$-functions at $s=0$. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of $S$-units can be described.
Overview From class field theory Extension classes Locally free class groups Tate sequences Recognizing $G$-modules Local analogue $\Omega m$ and the $G$-module structure of $E$ Artin $L$-functions at $s=0$ $q$-indices Parallel properties of$A \varphi$ and $A \varphi$ $\mathbb Q$-valued characters Representing the Chinburg class Small $S$ A cyclotomic example Notes Bibliography Subject index.