Discriminants of Hermitian R[G]-modules and Brauer’s Class Number Relation
نویسنده
چکیده
The purpose of this paper is to lay the foundations for a quantitative theory of relations among discriminants of hermitian RG-modules which are induced by character relations. This is accomplished by introducing an invariant δ(M) attached to an RG-module M which plays the role of a correction term in such relations and to study its functorial properties such as localization and induction theorems, behaviour with respect to exact sequences, triviality etc. By means of this formalism it is shown that this invariant may be computed in many cases. An application of this invariant is the class number relation of R. Brauer (1951) and, by using the formalism mentioned above, also that of Dirichlet (1842).
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تاریخ انتشار 2001