arXiv subjects

Sumito Hasegawa

Publications and source records attributed to Sumito Hasegawa.

3 recordsLinked to original sources

arXiv2026

The rationality problem for multinorm one tori, II

We investigate the stable and retract rationality of multinorm one tori associated to finite {é}tale algebras. Our results are organized according to the greatest common divisor $d$ of the degrees of the factors. We show that these tori are stably rational for $d=1$, and obtain a criterion for retract rationality that can be attributed to our previous results. For $d>1$, we provide sufficient conditions for the failure of retract rationality. We further generalize results of Endo--Miyata (1975) and Endo (2011) by giving an equivalent condition for multinorm one tori to be stably rational under the assumption that they split over Galois extensions with Galois groups in which all Sylow subgroups are cyclic. A similar result also holds when they split over dihedral Galois extensions.

math.AG↗

arXiv2026

The rationality problem for multinorm one tori

In this paper, we study the rationality problem for multinorm one tori, a natural generalization of norm one tori. For multinorm one tori that split over finite Galois extensions with nilpotent Galois group, we prove that stable rationality and retract rationality are equivalent, and give a criterion for the validity of the above two conditions. This generalizes the result of Endo (2011) on the rationality problem for norm one tori. To accomplish it, we introduce a generalization of character groups of multinorm one tori. Moreover, we establish systematic reduction methods originating in work of Endo (2001) for an investigation of the rationality problem for arbitrary multinorm one tori. In addition, we provide a new example for which the multinorm principle holds.

math.AG↗

arXiv2019

Rationality problem for norm one tori in small dimensions

We classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\geq 1)$ is a power of $2$ and $n=12, 14, 15$. Retract non-rationality of norm one tori for primitive $G\leq S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\leq S_n$ $(n=11,12,22,23,24)$ is also given.

math.AG↗