On the generalized Bykovskii presentation of Steinberg modules
Abstract
We study presentations of the virtual dualizing modules of special linear groups of number rings, the Steinberg modules. Bykovskii gave a presentation for the Steinberg modules of the integers, and our main result is a generalization of this presentation to the Gaussian integers and the Eisenstein integers. We also show that this generalization does not give a presentation for the Steinberg modules of several Euclidean number rings.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.10906
 arXiv:
 arXiv:2006.10906
 Bibcode:
 2020arXiv200610906K
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Group Theory;
 Mathematics  Geometric Topology;
 Mathematics  Number Theory;
 11F75 55N25 55R35 55U10
 EPrint:
 Minor revisions based on referee's comments. Accepted for publication at IMRN