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On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
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Bartel, Alex (2012) On Brauer–Kuroda type relations of S-class numbers in dihedral extensions. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol.2012 (No.668). pp. 211-244. doi:10.1515/CRELLE.2011.152 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/CRELLE.2011.152
Abstract
Let F/k be a Galois extension of number fields with dihedral Galois group of order 2q, where q is an odd integer. We express a certain quotient of S-class numbers of intermediate fields, arising from Brauer–Kuroda relations, as a unit index. Our formula is valid for arbitrary extensions with Galois group D2q and for arbitrary Galois-stable sets of primes S, containing the Archimedean ones. Our results have curious applications to determining the Galois module structure of the units modulo the roots of unity of a D2q-extension from class numbers and S-class numbers. The techniques we use are mainly representation theoretic and we consider the representation theoretic results we obtain to be of independent interest.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal für die reine und angewandte Mathematik (Crelles Journal) | ||||
Publisher: | Walter de Gruyter GmbH & Co. KG | ||||
ISSN: | 0075-4102 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol.2012 | ||||
Number: | No.668 | ||||
Page Range: | pp. 211-244 | ||||
DOI: | 10.1515/CRELLE.2011.152 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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