Index formulae for integral Galois modules

Bartel, A. and de Smit, B. (2013) Index formulae for integral Galois modules. Journal of the London Mathematical Society, 88(3), pp. 845-859. (doi: 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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bartel, Professor Alex
• Authors: Bartel, A., and de Smit, B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of the London Mathematical Society
• Publisher: Wiley
• ISSN: 0024-6107
• ISSN (Online): 1469-7750
• Published Online: 09 September 2013
• Copyright Holders: Copyright © 2013 London Mathematical Society
• First Published: First published in Journal of the London Mathematical Society 88(3):845-859
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher