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2007 Integral Springer Theorem for quaternionic forms
Luis Arenas-Carmona
Nagoya Math. J. 187: 157-174 (2007).

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.

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Luis Arenas-Carmona. "Integral Springer Theorem for quaternionic forms." Nagoya Math. J. 187 157 - 174, 2007.

Information

Published: 2007
First available in Project Euclid: 4 September 2007

zbMATH: 1161.11007
MathSciNet: MR2354559

Subjects:
Primary: 11E08 , 11E12 , 11E41

Rights: Copyright © 2007 Editorial Board, Nagoya Mathematical Journal

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Vol.187 • 2007
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