Injectivity and surjectivity of the Dress map

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• 作者：Ricardo G Rojas-Echenique ^{rojasecr@reed.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11E81 ; 19A22 ; 19G99 ; 14F42 ; 55P91
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：220
• 期：12
• 页码：3816-3820
• 全文大小：241 K

文摘

For a nontrivial finite Galois extension L/k$L/k$ (where the characteristic of k is different from 2) with Galois group G  , we prove that the Dress map h_L/k:A(G)→GW(k)$h_{L/k}:A(G)\to GW(k)$ is injective if and only if $L=k(\sqrt{\alpha })$ where α   is not a sum of squares in k^×$k^{\times }$. Furthermore, we prove that h_L/k$h_{L/k}$ is surjective if and only if k is quadratically closed in L  . As a consequence, we give strong necessary conditions for faithfulness of the Heller–Ormsby functor $c_{L/k}^{⁎}:{\mathrm{SH}}_G\to {\mathrm{SH}}_k$, as well as strong necessary conditions for fullness of $c_{L/k}^{⁎}$.