Capitulation, ambiguous classes and the cohomology of the units
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Publication:5459217
DOI10.1515/CRELLE.2007.092zbMath1226.11122arXivmath/0605586OpenAlexW2091791998MaRDI QIDQ5459217
Publication date: 25 April 2008
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0605586
Related Items (6)
Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ The Chevalley-Herbrand formula and the real abelian Main Conjecture (new criterion using capitulation of the class group) ⋮ On the arithmetic of modified idèle class groups ⋮ The Galois Brumer–Stark conjecture for SL2(𝔽3)-extensions ⋮ Cokernels of restriction maps and subgroups of norm one, with applications to quadratic Galois coverings ⋮ Čech cohomology and the capitulation kernel
Cites Work
- Some results on the capitulation problem
- Principal ideal theorems in the genus field for absolutely abelian extensions
- Ambiguous divisor classes in function fields
- Idéaux ambiges dans les corps de fonctions. (Ambiguous ideals in function fields)
- On the capitulation in the genus field of an abelian extension of an imaginary quadratic field
- Finite modules over non-semisimple group rings.
- On a quotient of the unramified Iwasawa module over an abelian number field. II.
- Galois groups of extensions of algebraic number fields with given ramification
- Some results related to Hilbert's theorem 94
- On Cohomology Groups of Units for Z p -Extensions
- A note on the ideal class group of the cyclotomic Zp-extension of a totally real number field
- On capitulation cokernels in Iwasawa theory
- On a quotient of the unramified Iwasawa module over an abelian number field
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