2023/02/13 by Hoshi, Akinari, Yamasaki, Aiichi
#11E72 #12F20 #13A50 #14E08 #20C10 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2302.06231
We give a complete answer to the rationality problem (up to stable k-equivalence) for norm one tori R(1)K/k(\mathbbGm) of K/k whose Galois closures L/k 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.