A new approach to classification of integral quadratic forms over dyadic local fields
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- by Constantin N. Beli PDF
- Trans. Amer. Math. Soc. 362 (2010), 1599-1617 Request permission
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
- Constantin N. Beli, Integral spinor norm groups over dyadic local fields, J. Number Theory 102 (2003), no. 1, 125–182. MR 1994477, DOI 10.1016/S0022-314X(03)00057-X
- Constantin N. Beli, Representations of integral quadratic forms over dyadic local fields, Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 100–112. MR 2237274, DOI 10.1090/S1079-6762-06-00165-X
- J. S. Hsia, Spinor norms of local integral rotations. I, Pacific J. Math. 57 (1975), no. 1, 199–206. MR 374029, DOI 10.2140/pjm.1975.57.199
- O. T. O’Meara, Introduction to quadratic forms, Die Grundlehren der mathematischen Wissenschaften, Band 117, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0152507, DOI 10.1007/978-3-642-62031-7
Additional Information
- Constantin N. Beli
- Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700Bucharest, Romania
- MR Author ID: 718695
- Email: raspopitu1@yahoo.com, Constantin.Beli@imar.ro
- 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. - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 1599-1617
- MSC (2000): Primary 11E08
- DOI: https://doi.org/10.1090/S0002-9947-09-04802-8
- MathSciNet review: 2563742