Skip Navigation

Journal of the London Mathematical Society 1994 49(3):417-441; doi:10.1112/jlms/49.3.417
© 1994 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Holland, D.
Right arrow Articles by Wilson, S. M. J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Factor Equivalence of Rings of Integers and Chinburg's Invariant in the Defect Class Group

D. Holland and S. M. J. Wilson

School of Mathematics, University Walk Bristol BS8 1TW
Department of Mathematical Sciences, University of Durham, Science Laboratories South Road, Durham DH1 3LE

Received 24 February 1992. Revision received 27 October 1992.

Let {Gamma} be a finite group. We introduce the factorizability defect, fd, defined on exact sequences in mod(Z{Gamma}).

Let C be the subcategory of mod (Z{Gamma}) of modules with finite projective dimension away from a finite set S of integer primes. We examine the defect class group Cl(Cfd) (the subgroup of locally trivial elements in the defect Grothendieck group, K0(Cfd)) and show that it is isomorphic to the direct sum class group ofC.

Let N/K be a Galois extension of algebraic number fields with group {Gamma} which is tamely ramified outside S. We show that [ON] — [OK{Gamma}] lies in Cl(Cfd) and equals the image of {Omega}(N/K,2), Chinburg's second invariant. We also show that if M and M' lie in C and [M] — [M'] isin Cl(Cfd) then M is factor equivalent to M' in a very strong sense. In particular ON is factor equivalent in this way to a free Z{Gamma}-module.

Most of this work was carried out while the first author was employed under a grant from the University of Durham's Special Projects Research Fund.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.