Galois Module Structure (Fields Institute Monographs, 2) - Hardcover

Victor P. Snaith

Hardcover

ISBN 10: 082180264X ISBN 13: 9780821802649

Publisher: American Mathematical Society, Fields Institute, 1994

Synopsis

Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have ``Hom-descriptions'' in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case. The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems. The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$.

About this title

Review

It will be useful for specialists inside and outside of this subject, as well as for graduate students. --Zentralblatt für Mathematik

Edition details

• Publisher: American Mathematical Society, Fields Institute
• Publication date: 1994
• Language: English
• ISBN 10: 082180264X
• ISBN 13: 9780821802649
• Binding: Hardcover
• Number of pages: 207