Abstract
We consider the problem of whether the norm one torus defined by a finite separable field extension is stably (or retract) rational over . This has already been solved for the case where is a Galois extension. In this paper, we solve the problem for the case where is a non-Galois extension such that the Galois group of the Galois closure of is nilpotent or metacyclic.
Citation
Shizuo Endo. "The rationality problem for norm one tori." Nagoya Math. J. 202 83 - 106, June 2011. https://doi.org/10.1215/00277630-1260459
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