Rationality problem for norm one tori for dihedral extensions
Algebraic Geometry
2023-11-21 v3 Number Theory
Rings and Algebras
Abstract
We give a complete answer to the rationality problem (up to stable -equivalence) for norm one tori of whose Galois closures are dihedral extensions with the aid of Endo and Miyata [EM75, Theorem 1.5, Theorem 2.3] and Endo [End11, Theorem 2.1]. By using a similar technique, we give refinements of the proof of stably rational cases of Endo and Miyata's theorems as an appendix of the paper.
Cite
@article{arxiv.2302.06231,
title = {Rationality problem for norm one tori for dihedral extensions},
author = {Akinari Hoshi and Aiichi Yamasaki},
journal= {arXiv preprint arXiv:2302.06231},
year = {2023}
}
Comments
11 pages, typos corrected, to appear in J. Algebra. arXiv admin note: text overlap with arXiv:1811.01676, arXiv:1910.01469, arXiv:1811.02145, arXiv:1210.4525, arXiv:2112.02280