Publication

Higher torsion in the Abelianization of the full Bianchi groups

Rahm, Alexander D.
Thumbnail Image
Files
Thumbnail Image
higher_torsion.pdf
Adobe PDF, 379.05 KB
Repository DOI
Publication Date
2013-09
Keywords
Imaginary quadratic integers, Elliptic curves, Homology, Psl2, Cohomology, Reduction
Type
Article
Downloads
Show all metadata
Citation
Rahm, AD (2013) 'Higher torsion in the Abelianization of the full Bianchi groups'. Lms Journal Of Computation And Mathematics, 16 :344-365.
Abstract
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.
Funder
|~|
Publisher
Cambridge University Press (Cambridge Journals Online)
Publisher DOI
DOI 10.1112/S1461157013000168
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
Collections
Mathematics (Scholarly Articles)