Triple linkage of quadratic Pfister forms

Adam Chapman; Andrew Dolphin; David B. Leep

doi:10.1007/s00229-017-0996-6

Triple linkage of quadratic Pfister forms

Adam Chapman, Andrew Dolphin, David B. Leep

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Given a field F of characteristic 2, we prove that if every three quadratic n-fold Pfister forms have a common quadratic (n- 1) -fold Pfister factor then Iqn+1F=0. As a result, we obtain that if every three quaternion algebras over F share a common maximal subfield then u(F) is either 0, 2 or 4. We also prove that if F is a nonreal field with char(F)≠2 and u(F) = 4 , then every three quaternion algebras share a common maximal subfield.

Original language	English
Pages (from-to)	435-443
Number of pages	9
Journal	Manuscripta Mathematica
Volume	157
Issue number	3-4
DOIs	https://doi.org/10.1007/s00229-017-0996-6
State	Published - Nov 1 2018

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Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

General Mathematics

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AB - Given a field F of characteristic 2, we prove that if every three quadratic n-fold Pfister forms have a common quadratic (n- 1) -fold Pfister factor then Iqn+1F=0. As a result, we obtain that if every three quaternion algebras over F share a common maximal subfield then u(F) is either 0, 2 or 4. We also prove that if F is a nonreal field with char(F)≠2 and u(F) = 4 , then every three quaternion algebras share a common maximal subfield.

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Triple linkage of quadratic Pfister forms

Abstract

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