Work

Non‐integrality of some Steinberg modules

Year: 2020

Type: article

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 apartment classes. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartment classes 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.

Source: Journal of Topology

DOI: 10.1112/topo.12132

Authors: Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson, Dan Yasaki

Institutions: Purdue University West Lafayette, University of Michigan, University of North Carolina at Greensboro

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Homological Stability and Its Generalizations