Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 187 (2007), 157-174.
Integral Springer Theorem for quaternionic forms
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.
Nagoya Math. J., Volume 187 (2007), 157-174.
First available in Project Euclid: 4 September 2007
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Arenas-Carmona, Luis. Integral Springer Theorem for quaternionic forms. Nagoya Math. J. 187 (2007), 157--174. https://projecteuclid.org/euclid.nmj/1188913898