2022年9月
Norm one Tori and Hasse norm principle
Mathematics of Computation
- ,
- ,
- 巻
- 91
- 号
- 337
- 開始ページ
- 2431
- 終了ページ
- 2458
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1090/mcom/3735
- 出版者・発行元
- American Mathematical Society (AMS)
<p>Let be a field and be an algebraic -torus. In 1969, over a global field , Voskresenskiǐ proved that there exists an exact sequence where is the kernel of the weak approximation of , is the Shafarevich-Tate group of , is a smooth -compactification of , , is the Picard group of and stands for the Pontryagin dual. On the other hand, in 1963, Ono proved that for the norm one torus of , if and only if the Hasse norm principle holds for . First, we determine for algebraic -tori up to dimension . Second, we determine for norm one tori with and . We also show that for when the Galois group of the Galois closure of is the Mathieu group with . Third, we give a necessary and sufficient condition for the Hasse norm principle for with and . As applications of the results, we get the group of -equivalence classes over a local field via Colliot-Thélène and Sansuc’s formula and the Tamagawa number over a number field via Ono’s formula .</p>
- リンク情報
- ID情報
-
- DOI : 10.1090/mcom/3735
- ISSN : 0025-5718
- eISSN : 1088-6842
- ORCIDのPut Code : 109440357