Non-integrality of some Steinberg modules
Algebraic Topology
2020-09-28 v2 Geometric Topology
Number Theory
Abstract
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ring is Euclidean. We also construct new cohomology classes in the top dimensional cohomology group of the special linear group of some quadratic imaginary number rings.
Cite
@article{arxiv.1810.07683,
title = {Non-integrality of some Steinberg modules},
author = {Jeremy Miller and Peter Patzt and Jennifer C. H. Wilson and Dan Yasaki},
journal= {arXiv preprint arXiv:1810.07683},
year = {2020}
}
Comments
17 pages. To appear in Journal of Topology