On the generalized Bykovskii presentation of Steinberg modules
Algebraic Topology
2023-06-13 v2 Group Theory
Geometric Topology
Number Theory
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.
Cite
@article{arxiv.2006.10906,
title = {On the generalized Bykovskii presentation of Steinberg modules},
author = {Alexander Kupers and Jeremy Miller and Peter Patzt and Jennifer C. H. Wilson},
journal= {arXiv preprint arXiv:2006.10906},
year = {2023}
}
Comments
Minor revisions based on referee's comments. Accepted for publication at IMRN