稳定的理性和周期性

David J Saltman
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引用次数: 0

摘要

关于素度$p$的除法代数,有两个悬而未决的问题。第一个问题是它们是否是循环的,或者等价于交叉积。第二个问题是通用除法代数$UD(F,p)$的中心$Z(F,p)$是否是在$F$上稳定有理的。当 $F$ 特性为 0 且包含一个一的基元 $p$ 根时,我们证明这两个问题之间存在联系。也就是说,我们证明了如果 $Z(F,p)$ 不是稳定有理的,那么 $UD(F,p)$ 就不是循环的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stable Rationality and Cyclicity
There are two outstanding questions about division algebras of prime degree $p$. The first is whether they are cyclic, or equivalently crossed products. The second is whether the center, $Z(F,p)$, of the generic division algebra $UD(F,p)$ is stably rational over $F$. When $F$ is characteristic 0 and contains a primitive $p$ root of one, we show that there is a connection between these two questions. Namely, we show that if $Z(F,p)$ is not stably rational then $UD(F,p)$ is not cyclic.
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