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Index formulae for integral Galois modules
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Bartel, Alex and de Smit, B. (2013) Index formulae for integral Galois modules. Journal of the London Mathematical Society, Volume 88 (Number 3). pp. 845-859. doi:10.1112/jlms/jdt033 ISSN 0024-6107.
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Official URL: http://dx.doi.org/10.1112/jlms/jdt033
Abstract
We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mordell–Weil groups of elliptic curves over number fields. These formulae link the respective Galois module structure to other arithmetic invariants, such as class numbers, or Tamagawa numbers and Tate–Shafarevich groups. This is a generalization of known results on units to other Galois modules and to many more Galois groups, and at the same time a unification of the approaches hitherto developed in the case of units.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Galois modules (Algebra), Galois theory | ||||
Journal or Publication Title: | Journal of the London Mathematical Society | ||||
Publisher: | Oxford University Press | ||||
ISSN: | 0024-6107 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 88 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 845-859 | ||||
DOI: | 10.1112/jlms/jdt033 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Great Britain. Royal Commission for the Exhibition of 1851 |
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