Bulletin of the Belgian Mathematical Society - Simon Stevin

Harrison's criterion, Witt equivalence and reciprocity equivalence

N. Grenier-Boley

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 3 (2009), 509-523.

Dates
First available in Project Euclid: 1 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1251832376

Digital Object Identifier
doi:10.36045/bbms/1251832376

Mathematical Reviews number (MathSciNet)
MR2566871

Zentralblatt MATH identifier
1196.11060

Subjects
Primary: 11E39: Bilinear and Hermitian forms
Secondary: 11E81: Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]

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

Citation

Grenier-Boley, N. Harrison's criterion, Witt equivalence and reciprocity equivalence. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 3, 509--523. doi:10.36045/bbms/1251832376. https://projecteuclid.org/euclid.bbms/1251832376


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