Retract Rationality and Algebraic Tori
Retract Rationality and Algebraic Tori
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撤回理性和代数环
DOI：
10.4153/s0008439519000079
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
F. Scavia
中科院分区：
文献类型：
--
作者：
F. Scavia
摘要对于任意素数$p$和域$k$，我们用特征格刻画了代数$k$环面的$p$-可缩合理性。我们证明了$k$-环面是可伸缩有理的当且仅当它是$p$-可伸缩有理对于每一个素数$p$，并且对于一组乘型$G$的可伸缩有理的Noether问题对于$G$有一个肯定的答案当且仅当$p$-可伸缩有理对于$G$的Noether问题对于所有$p$有一个正的答案。对于每一个有限素数集，我们给出了环面$p$-伸缩有理当且仅当$p\notin S$的例子。
Abstract For any prime number $p$ and field $k$, we characterize the $p$-retract rationality of an algebraic $k$-torus in terms of its character lattice. We show that a $k$-torus is retract rational if and only if it is $p$-retract rational for every prime $p$, and that the Noether problem for retract rationality for a group of multiplicative type $G$ has an affirmative answer for $G$ if and only if the Noether problem for $p$-retract rationality for $G$ has a positive answer for all $p$. For every finite set of primes $S$ we give examples of tori that are $p$-retract rational if and only if $p\notin S$.