Types of linkage of quadratic Pfister forms

JOURNAL OF NUMBER THEORY

卷:199

Article

Chapman, Adam¹  Dolphin, Andrew² 

[1] Tel Hai Acad Coll, Dept Comp Sci, IL-12208 Upper Galilee, Israel

[2] Univ Antwerp, Dept Wiskunde Informat, Antwerp, Belgium

关键词: Kato-Milne cohomology;    Fields of positive characteristic;    Quadratic forms;    Pfister forms;    Quaternion algebras;    Linkage;   

DOI  :  10.1016/j.jnt.2018.11.017

来源: Elsevier

【 摘 要 】

Given a field F of positive characteristic p, theta is an element of H-p(n-1)(F) and beta,gamma is an element of Fx, we prove that if the symbols theta <^> d beta/beta and theta <^> d gamma/gamma in H-p(n)(F) share the same factors in H-p(1) (F) then the symbol theta <^> d beta/beta <^>d gamma/gamma in H-p(n+1)(F) is trivial. We conclude that when p = 2, every two totally separably (n - 1)-linked n-fold quadratic Pfister forms are inseparably (n - 1)-linked. We also describe how to construct non-isomorphic n-fold Pfister forms which are totally separably (or inseparably) (n - 1)-linked, i.e. share all common (n 1)-fold quadratic (or bilinear) Pfister factors. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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