English

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

R2 v1 2026-06-23T16:27:11.490Z