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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Witt equivalence of global fields. II. Relative quadratic extensions


Author: Kazimierz Szymiczek
Journal: Trans. Amer. Math. Soc. 343 (1994), 277-303
MSC: Primary 11E12; Secondary 11E08, 11E81
MathSciNet review: 1176087
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Abstract: This paper explores the consequences of the Hasse Principle for Witt equivalence of global fields in the case of relative quadratic extensions. We are primarily interested in generating the Witt equivalence classes of quadratic extensions of a given number field, and we study the structure of the class, the number of classes, and the structure of the set of classes. Along the way, we reprove several results obtained earlier in the absolute case of the rational ground field, giving unified and short proofs based on the Hasse Principle.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1176087-X
PII: S 0002-9947(1994)1176087-X
Keywords: Witt equivalence, relative quadratic extensions, Hasse principle
Article copyright: © Copyright 1994 American Mathematical Society