Titlebook: Galois Module Structure of Algebraic Integers; Albrecht Fr?hlich Book 1983 Springer-Verlag Berlin Heidelberg 1983 Algebraische Zahlentheor

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Root Number Values, from the fact that the root numbers provide a full set of invariants for stable Galois module structure of rings of integers, and also from the implications on zeros of Dedekind zeta functions at . = 1/2. For this see the remark in I §1.

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Classgroups and Determinants,r . is a number field, O its ring of algebraic integers, . a finite group and 21 an o-order in .. With appropriate changes (specifically replacing . by a certain Grothendieck group) the contents of this section apply equally well to any arbitrary semisimple finite dimensional algebra in place of . but we shall avoid such unnecessary generality.

祖先

Introduction,h in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin .-functions. We shall concentrate on the topic which has been at

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DEMUR

Classgroups and Determinants,kground see note [1]. There are three basic steps involved. The first leads to a K-theoretic interpretation of the class group, in terms of an exact sequence. We state the relevant definitions and results, but will not prove them — for a detailed discussion see e.g., [F24] (Chap. 1). The second step

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樸素

Root Number Values,s on the possible distributions of root number values and on the densities of such distributions. The interest in this type of problem comes of course from the fact that the root numbers provide a full set of invariants for stable Galois module structure of rings of integers, and also from the impli