Author | Frรถhlich, Albrecht. author |
---|---|
Title | Galois Module Structure of Algebraic Integers [electronic resource] / by Albrecht Frรถhlich |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1983 |
Connect to | http://dx.doi.org/10.1007/978-3-642-68816-4 |
Descript | X, 266 p. online resource |
Notation and Conventions -- I. Survey of Results -- ยง1. The Background -- ยง2. The Classgroup -- ยง3. Ramification and Module Structure -- ยง4. Resolvents -- ยง5. L-Functions and Galois Gauss Sums -- ยง6. Symplectic Root Numbers and the Class UN/K -- ยง7. Some Problems and Examples -- Notes to Chapter I -- II. Classgroups and Determinants -- ยง1. Hom-Description -- ยง2. Localization -- ยง3. Change in Basefield and Change in Group -- ยง4. Reduction mod l and Some Computations -- ยง5. The Logarithm for Group Rings -- ยง6. Galois Properties of the Determinant -- Notes to Chapter II -- III. Resolvents, Galois Gauss Sums, Root Numbers, Conductors -- ยง1. Preliminaries -- ยง2. Localization of Galois Gauss Sums and of Resolvents -- ยง3. Galois Action -- ยง4. Signatures -- ยง5. The Local Main Theorems -- ยง6. Non-Ramified Base Field Extension -- ยง7. Abelian Characters, Completion of Proofs -- ยง8. Module Conductors and Module Resolvents -- Notes to Chapter III -- IV. Congruences and Logarithmic Values -- ยง1. The Non-Ramified Characteristic -- ยง2. Proof of Theorem 31 -- ยง3. Reduction Steps for Theorem 30 -- ยง4. Strategy for Theorem 32 -- ยง5. Gauss Sum Logarithm -- ยง6. The Congruence Theorems -- ยง7. The Arithmetic Theory of Tame Local Galois Gauss Sums -- Notes to Chapter IV -- V. Root Number Values -- ยง1. The Arithmetic of Quaternion Characters -- ยง2. Root Number Formulae -- ยง3. Density Results -- ยง4. The Distribution Theorem -- VI. Relative Structure -- ยง1. The Background -- ยง2. Galois Module Structure and the Embedding Problem -- ยง3. An Example -- ยง4. Generalized Kummer Theory -- ยง5. The Generalized Class Number Formula and the Generalized Stickelberger Relation -- Literature List -- List of Theorems -- Some Further Notation