Quartic polynomials and the Hasse norm theorem modulo squares

JOURNAL OF NUMBER THEORY

卷:165

Article

Sivatski, A. S.¹ 

[1] Univ Fed Ceara, Dept Matemat, Fortaleza, Ceara, Brazil

关键词: Brauer group;    Cup-product;    Field extension;    The u-invariant;    The Hasse norm theorem;   

DOI  :  10.1016/j.jnt.2016.01.022

来源: Elsevier

【 摘 要 】

Let F be a field, char F not equal 2, L/F a quartic field extension. Define by G(L/F) the group of elements r is an element of F* such that D boolean OR (r) = 0 for any regular field extension K/F and any D is an element of 2Br(KL/K). We show that G(L/F) = F*2N(L)/L-F*. As a consequence we prove that the Hasse norm theorem modulo squares holds for L/F. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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