期刊論文
| 學年 | 98 |
|---|---|
| 學期 | 1 |
| 出版（發表）日期 | 2010-01-01 |
| 作品名稱 | Noether’s Problem and the Unramified Brauer Group for Groups of Order 64 |
| 作品名稱（其他語言） | |
| 著者 | Chu, Huah; Hu, Shou-Jen; Kang, Ming-Chang; Kunyavskii, Boris E. |
| 單位 | 淡江大學數學學系 |
| 出版者 | Oxford: Oxford University Press |
| 著錄名稱、卷期、頁數 | International Mathematics Research Notices 2010(12), pp.2329-2366 |
| 摘要 | Let K be any field and G be a finite group acting on the rational function field K(xg : g ∈ G) by h ⋅ xg = xhg for any g, h ∈ G. Define K(G) = K(xg : g ∈ G)G. Noether’s problem asks whether K(G) is rational (purely transcendental) over K. For any prime number p, Bogomolov shows that there is some group G of order p6 with B0(G) ≠ 0, where B0(G) is the unramified Brauer group of ℂ(G), which is the subgroup of H2(G, ℚ/ℤ) consisting of cohomology classes whose restrictions to all bicyclic subgroups are zero. As a consequence, ℂ(G) is not rational over ℂ. In this paper, we will classify all the groups G of order 64 with B0(G) ≠ 0; for groups G satisfying B0(G) = 0, we will show that ℂ(G) is rational except possibly for five cases. |
| 關鍵字 | |
| 語言 | en |
| ISSN | 1073-7928; 1687-0247 |
| 期刊性質 | 國外 |
| 收錄於 | SCI |
| 產學合作 | |
| 通訊作者 | Kang, Ming-Chang |
| 審稿制度 | |
| 國別 | GBR |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/58759 ) |