Higher torsion in the Abelianization of the full Bianchi groups

被引:10
|
作者
Rahm, Alexander D. [1 ]
机构
[1] Natl Univ Ireland, Dept Math, Galway, Ireland
关键词
ELLIPTIC-CURVES; HOMOLOGY; PSL2; COHOMOLOGY; REDUCTION;
D O I
10.1112/S1461157013000168
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Denote by Q(root-m), with m a square-free positive integer, an imaginary quadratic number field, and by O-m its ring of integers. The Bianchi groups are the groups SL2(O-m). In the literature, so far there have been no examples of p-torsion in the integral homology of the full Bianchi groups, for p a prime greater than the order of elements of finite order in the Bianchi group, which is at most 6. However, extending the scope of the computations, we can observe examples of torsion in the integral homology of the quotient space, at prime numbers as high as for instance p = 80 737 at the discriminant -1747.
引用
收藏
页码:344 / 365
页数:22
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