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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

A new approach to classification of integral quadratic forms over dyadic local fields


Author: Constantin N. Beli
Journal: Trans. Amer. Math. Soc. 362 (2010), 1599-1617
MSC (2000): Primary 11E08
Published electronically: October 6, 2009
MathSciNet review: 2563742
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Abstract: In 1963, O'Meara solved the classification problem for lattices over dyadic local fields in terms of Jordan decompositions. In this paper we translate his result in terms of good BONGs. BONGs (bases of norm generators) were introduced in 2003 as a new way of describing lattices over dyadic local fields. This result and the notions we introduce here are a first step towards a solution of the more difficult problem of representations of lattices over dyadic fields.


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Additional Information

Constantin N. Beli
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania
Email: raspopitu1@yahoo.com, Constantin.Beli@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04802-8
Received by editor(s): November 14, 2006
Received by editor(s) in revised form: April 8, 2008
Published electronically: October 6, 2009
Additional Notes: This research was partially supported by the Contract 2-CEx06-11-20.
In Beli (2006) this paper was announced under the title “BONG version of O’Meara’s 93:28 theorem". We changed the title at the referee’s suggestion.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.