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Determining Fitting ideals of minus class groups via the equivariant Tamagawa number conjecture

Part of: Algebraic number theory: global fields Whitehead groups and $K_1$

Published online by Cambridge University Press:  01 November 2007

Cornelius Greither
Cornelius Greither*
Affiliation:
Fakultät Informatik, Universität der Bundeswehr München, 85577 Neubiberg, Germany (email: [email protected])
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Abstract

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We assume the validity of the equivariant Tamagawa number conjecture for a certain motive attached to an abelian extension K/k of number fields, and we calculate the Fitting ideal of the dual of clK− as a Galois module, under mild extra hypotheses on K/k. This builds on concepts and results of Tate, Burns, Ritter and Weiss. If k is the field of rational numbers, our results are unconditional.

Keywords

Tate sequencesGalois modulesFitting idealsequivariant L-values

MSC classification

Secondary: 11R29: Class numbers, class groups, discriminants 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers 11R42: Zeta functions and $L$-functions of number fields 19B28: $K_1$ of group rings and orders
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1399 - 1426
Copyright
Copyright © Foundation Compositio Mathematica 2007