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Bulletin of the London Mathematical Society Advance Access originally published online on April 3, 2009
Bulletin of the London Mathematical Society 2009 41(3):541-548; doi:10.1112/blms/bdp030
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© 2009 London Mathematical Society

Capitulation for locally free class groups of orders of group algebras over number fields

Cornelius Greither

Fakultät für Informatik
Institut für theoretische Informatik und Mathematik
Universität der Bundeswehr München
85577 Neubiberg
Germany

Henri Johnston

St. Hugh's College
St. Margaret's Road
Oxford
OX2 6LE
United Kingdom
henri@maths.ox.ac.uk

Received 29 January 2008. Revision received 18 February 2008.

We prove a capitulation result for locally free class groups of orders of group algebras over number fields. This result allows some control over ramification, and so, as a corollary, we obtain an ‘arithmetically disjoint capitulation result’ for the Galois module structure of rings of integers.

2000 Mathematics Subject Classification 11R65 (primary), 11R33 (secondary).

The second author was supported by a grant from the Deutscher Akademischer Austausch Dienst.


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