On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
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Alex Bartel
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.
©[2012] by Walter de Gruyter Berlin Boston
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- Overconvergent Witt vectors
- Special subvarieties of Drinfeld modular varieties
- Explicit uniform estimation of rational points I. Estimation of heights
- Explicit uniform estimation of rational points II. Hypersurface coverings
- Pieri rules for the K-theory of cominuscule Grassmannians
- The Hörmander multiplier theorem for multilinear operators
- Quantum cluster variables via Serre polynomials
- Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
- On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
Articles in the same Issue
- Overconvergent Witt vectors
- Special subvarieties of Drinfeld modular varieties
- Explicit uniform estimation of rational points I. Estimation of heights
- Explicit uniform estimation of rational points II. Hypersurface coverings
- Pieri rules for the K-theory of cominuscule Grassmannians
- The Hörmander multiplier theorem for multilinear operators
- Quantum cluster variables via Serre polynomials
- Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
- On Brauer–Kuroda type relations of S-class numbers in dihedral extensions
