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.
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Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Gewicht
ISBN-13
978-0-8218-0265-6 (9780821802656)
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Schweitzer Klassifikation
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.
