| 函数域的K_2群的挠元 |
| |
| 引用本文： | 徐克舰,刘敏. 函数域的K_2群的挠元[J]. 数学学报, 2010, 53(3): 611-616 |
| |
| 作者姓名： | 徐克舰 刘敏 |
| |
| 作者单位： | 青岛大学数学科学学院;中国科学院数学与系统科学研究院; |
| |
| 基金项目： | 国家自然科学基金资助项目(10871106) |
| |
| 摘 要： | 设F是域,令G_n(F)={{a,φ_n(a)}∈K_2(F)| a,Φ_n(a)∈F~*},这里Φ_n(x)是n次分圆多项式.使用函数域的ABC定理证明了若F是常数域为k函数域,l≠ch(k)是素数,则对n≥3且l>2或n>3且l=2,G_(ln)(F)不是K_2(F)的子群.由此部分地证实了Browkin的猜想.
|
| 关 键 词： | 函数域 分圆元素 Milnor K_2群 |
| 收稿时间： | 2009-03-16 |
| 修稿时间： | 2009-12-22 |
On the Torsion in K2 of a Function Field |
| |
| Ke Jian XU College of Mathematics,Qingdao University,Qingdao ,P.R.China Academy of Mathematics , Systems Science,Chinese Academy of Sciences,Beijing ,P.R.China. On the Torsion in K2 of a Function Field[J]. Acta Mathematica Sinica, 2010, 53(3): 611-616 |
| |
| Authors: | Ke Jian XU College of Mathematics Qingdao University Qingdao P.R.China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing P.R.China |
| |
| Affiliation: | 1. College of Mathematics, Qingdao University, Qingdao 266071, P. R. China;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China |
| |
| Abstract: | Let F be a field and letGn(F)={{a, Φn(a)} ∈K2(F)|a,Φn(a) ∈ F*}, where Φn(x) denotes the n-th cyclotomic polynomial. If F is a function field with perfect constant field k and l≠ch(k) a prime number, it is proved by using the ABC theorem for function fields that Gln(F) is not a subgroup of K2(F) if n≥3 and l>2 or n>3 and l=2, which confirms a conjecture of Browkin partially. |
| |
| Keywords: | function field cyclotomic element Milnor K_2-group |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
|
点击此处可从《数学学报》下载全文 |
|
