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August 2009 Harrison's criterion, Witt equivalence and reciprocity equivalence
N. Grenier-Boley
Bull. Belg. Math. Soc. Simon Stevin 16(3): 509-523 (August 2009). DOI: 10.36045/bbms/1251832376


Harrison's criterion characterizes the isomorphy of the Witt rings of two fields in terms of properties of these fields. In this article, we discuss about the existence of such characterizations for the isomorphism of Witt groups of hermitian forms over certain algebras with involution. In the cases where we consider the Witt group of a quadratic extension with its non-trivial automorphism or the Witt group of a quaternion division algebra with its canonical involution, such criteria are proved. In the framework of global fields, these criteria are reformulated in terms of properties involving certain real places of the considered fields.


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N. Grenier-Boley. "Harrison's criterion, Witt equivalence and reciprocity equivalence." Bull. Belg. Math. Soc. Simon Stevin 16 (3) 509 - 523, August 2009.


Published: August 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1196.11060
MathSciNet: MR2566871
Digital Object Identifier: 10.36045/bbms/1251832376

Primary: 11E39
Secondary: 11E81

Keywords: algebras with involution , Harrison's criterion , reciprocity equivalence , Witt equivalence

Rights: Copyright © 2009 The Belgian Mathematical Society


Vol.16 • No. 3 • August 2009
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