By Albrecht Fröhlich

ISBN-10: 1468467409

ISBN-13: 9781468467406

ISBN-10: 1468467425

ISBN-13: 9781468467420

These notes are an accelerated and up-to-date model of a process lectures which I gave at King's university London in the course of the summer season time period 1979. the most subject is the Hermitian classgroup of orders, and particularly of staff jewelry. so much of this paintings is released right here for the 1st time. the first motivation got here from the relationship with the Galois module constitution of jewelry of algebraic integers. The critical objective used to be to put the theoretical foundation for attacking what can be known as the "converse challenge" of Galois module constitution thought: to specific the symplectic neighborhood and worldwide root numbers and conductors as algebraic invariants. a prior variation of those notes used to be circulated privately between a number of collaborators. in keeping with this, and following a partial resolution of the matter by means of the writer, Ph. Cassou-Nogues and M. Taylor succeeded in acquiring a whole answer. In a special course J. Ritter released a paper, answering convinced personality theoretic questions raised within the previous model. i personally disapprove of "secret circulation", however the strain of different paintings resulted in a hold up in booklet; i'm hoping this quantity will make amends. One benefit of the hold up is that the proper contemporary paintings may be incorporated. In a feeling this can be a spouse quantity to my fresh Springer-Ergebnisse-Bericht, the place the Hermitian concept was once no longer handled. Our strategy is through "Hom-groups", analogous to that in fresh paintings on in the neighborhood unfastened classgroups.