Factor equivalence of Galois modules and regulator constants

Bartel, A. (2014) Factor equivalence of Galois modules and regulator constants. International Journal of Number Theory, 10(1), pp. 1-12. (doi: 10.1142/S1793042113500772)

Abstract

We compare two approaches to the study of Galois module structures: on the one hand, factor equivalence, a technique that has been used by Fröhlich and others to investigate the Galois module structure of rings of integers of number fields and of their unit groups, and on the other hand, regulator constants, a set of invariants attached to integral group representations by Dokchitser and Dokchitser, and used by the author, among others, to study Galois module structures. We show that the two approaches are in fact closely related, and interpret results arising from these two approaches in terms of each other. We then use this comparison to derive a factorizability result on higher K-groups of rings of integers, which is a direct analogue of a theorem of de Smit on S-units.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bartel, Professor Alex
• Authors: Bartel, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Journal of Number Theory
• Publisher: World Scientific Publishing
• ISSN: 1793-0421
• ISSN (Online): 1793-7310
• Published Online: 18 September 2013
• Copyright Holders: Copyright © 2013 World Scientific Publishing
• First Published: First published in International Journal of Number Theory 10(1):1-12
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher