Quartic polynomials and the Hasse norm theorem modulo squares

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• 作者：A.S. Sivatski ^{alexander.sivatski@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11E04 ; 11E81
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：165
• 期：Complete
• 页码：58-66
• 全文大小：280 K

文摘

Let F   be a field, $\mathrm{char}F\ne 2$, L/F$L/F$ a quartic field extension. Define by G_L/F$G_{L/F}$ the group of elements r∈F^⁎$r\in F^{⁎}$ such that D∪(r)=0$D\cup (r)=0$ for any regular field extension K/F$K/F$ and any $D\in {}_2\mathrm{Br}(KL/K)$. We show that 05bc6d9ec6b78e162b45cf0ba" title="Click to view the MathML source">G_L/F=F^⁎2N_L/FL^⁎$G_{L/F}={F^{⁎}}^2{N}_{L/F}{L}^{⁎}$. As a consequence we prove that the Hasse norm theorem modulo squares holds for L/F$L/F$.