| Uniform Boundedness of Torsion Subgroups of Linear Groups |
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| 作者姓名： | Bin Yong SUN |
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| 作者单位： | Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China |
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| 基金项目： | Supported by Tianyuan Mathematics Foundation of NSFC （Grant No. 10626050）, and the Knowledge Innovation Program of the Chinese Academy of Sciences |
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| 摘 要： | The torsion conjecture says： for any abelian variety A defined over a number field k, the order of the torsion subgroup of A（k） is bounded by a constant C（k,d） which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over Q,Г is a torsion subgroup of G（k）. Then the order of Г is bounded by a constant C＇（k, d） which depends only on k and the dimension d of G.
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| 关 键 词： | 线性群 线性代数群 有限子群 曲率子群 |
| 文章编号： | 10.1007/s10114-007-1016-7 |
| 收稿时间： | 2005-11-07 |
| 修稿时间： | 2006-12-21 |
Uniform boundedness of torsion subgroups of linear groups |
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| Bin Yong SUN.Uniform Boundedness of Torsion Subgroups of Linear Groups[J].Acta Mathematica Sinica,2008,24(2):305-310. |
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| Authors: | Bin Yong Sun |
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| Institution: | (1) Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China |
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| Abstract: | The torsion conjecture says: for any abelian variety A defined over a number field k, the order of the torsion subgroup of A(k) is bounded by a constant C(k, d) which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that
the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over ℚ, Γ is a torsion subgroup of G(k). Then the order of Γ is bounded by a constant C′(k, d) which depends only on k and the dimension d of G.
Supported by Tianyuan Mathematics Foundation of NSFC (Grant No. 10626050), and the Knowledge Innovation Program of the Chinese
Academy of Sciences |
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| Keywords: | linear algebraic group finite subgroup torsion conjecture torsion subgroup |
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