4 papers
Multiplicative -ic forms on algebraic varieties arising from Thaine's generalized Jacobi sums
Akinari Hoshi, Kazuki Kanai
We study generalized Jacobi sums, cyclotomic numbers, and -compositions in Thaine's framework, and prove new multiplicative identities extending Davenport and Hasse's lifting th…
The rationality problem for multinorm one tori, II
Sumito Hasegawa, Kazuki Kanai, Yasuhiro Oki
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…
The rationality problem for multinorm one tori
Sumito Hasegawa, Kazuki Kanai, Yasuhiro Oki
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 w…
Norm one tori and Hasse norm principle, III: Degree case
Akinari Hoshi, Kazuki Kanai, Aiichi Yamasaki
Let be a field, be an algebraic -torus, be a smooth -compactification of and be the Picard group of $\overline{X}=X\times_k\overline…