Multiplicative Galois Module Structure

Based on a short course on the Galois structure of $S$-units that was given at The Fields Institute in the fall of 1993, this book features the main theme that this structure should be determined by class field theory, in its cohomological form, and by the behavior of Artin $L$-functions at $s=0$.

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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.