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Integral Springer Theorem for Quaternionic Forms

Published online by Cambridge University Press:  11 January 2016

Luis Arenas-Carmona
Luis Arenas-Carmona*
Affiliation:
Universidad de Chile, Facultad de Ciencias, Casilla 653, Santiago, Chile, learenas@uchile.cl
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Abstract

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J. S. Hsia has conjectured an arithmetical version of Springer Theorem, which states that no two spinor genera in the same genus of integral quadratic forms become identified over an odd degree extension. In this paper we prove by examples that the corresponding result for quaternionic skew-hermitian forms does not hold in full generality. We prove that it does hold for unimodular skew-hermitian lattices under all extensions and for lattices whose discriminant is relatively prime to 2 under Galois extensions.

Keywords

11E4111E0811E12
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 187 , September 2007 , pp. 157 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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