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- W2070970727 abstract "Let $k$ be an infinite field. The notion of retract $k$-rationality was introduced by Saltman in the study of Noether's problem and other rationality problems. We will investigate the retract rationality of a field in this paper. Theorem 1. Let $ksubset Ksubset L$ be fields. If $K$ is retract $k$-rational and $L$ is retract $K$-rational, then $L$ is retract $k$-rational. Theorem 2. For any finite group $G$ containing an abelian normal subgroup $H$ such that $G/H$ is a cyclic group, for any complex representation $G to GL(V)$, the fixed field $bm{C}(V)^G$ is retract $bm{C}$-rational. Theorem 3. If $G$ is a finite group, then all the Sylow subgroups of $G$ are cyclic if and only if $bm{C}_{alpha}(M)^G$ is retract $bm{C}$-rational for all $G$-lattices $M$, for all short exact sequences $alpha : 0 to bm{C}^{times} to M_{alpha} to M to 0$. Because the unramified Brauer group of a retract $bm{C}$-rational field is trivial, Theorem 2 and Theorem 3 generalize previous results of Bogomolov and Barge respectively (see Theorem ref{t5.9} and Theorem ref{t6.1})." @default.
- W2070970727 created "2016-06-24" @default.
- W2070970727 creator A5038464497 @default.
- W2070970727 date "2009-11-12" @default.
- W2070970727 modified "2023-09-27" @default.
- W2070970727 title "Retract Rational Fields" @default.
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- W2070970727 doi "https://doi.org/10.48550/arxiv.0911.2521" @default.
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