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A new approach to classification of integral quadratic forms over dyadic local fields
Author(s):
Constantin
N.
Beli
Journal:
Trans. Amer. Math. Soc.
362
(2010),
1599-1617.
MSC (2000):
Primary 11E08
Posted:
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.
References:
-
- 1.
- C. N. Beli, Integral spinor norms over dyadic local fields, J. Number Theory 102 (2003) 125-182. MR 1994477 (2004i:11030)
- 2.
- C.N Beli, Representations of integral quadratic forms over dyadic local fields, Electronic Research Announcements of the American Mathematical Society 12, 100-112, electronic only (2006). MR 2237274 (2007m:11054)
- 3.
- J. S. Hsia, Spinor norms of local integral rotations I, Pacific J. Math., Vol. 57 (1975), 199 - 206. MR 0374029 (51:10229)
- 4.
- O. T. O'Meara, Introduction to Quadratic Forms, Springer-Verlag, Berlin (1963). MR 0152507 (27:2485)
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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:
10.1090/S0002-9947-09-04802-8
PII:
S 0002-9947(09)04802-8
Received by editor(s):
November 14, 2006
Received by editor(s) in revised form:
April 8, 2008
Posted:
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.
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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