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Integral Springer Theorem for Quaternionic Forms

Published online by Cambridge University Press:  11 January 2016


Luis Arenas-Carmona
Affiliation:
Universidad de Chile, Facultad de Ciencias, Casilla 653, Santiago, Chile, learenas@uchile.cl
Corresponding
E-mail address:

Abstract

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.


Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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