Work

On rank filtrations of algebraic $K$-theory and Steinberg modules

Year: 2025

Type: article

Abstract: Motivated by his work on the stable rank filtration of algebraic K -theory spectra, Rognes defined a simplicial complex called the common basis complex and conjectured that this complex is highly connected for local rings and Euclidean domains. We prove this conjecture in the case of fields. Our methods give a novel description of this common basis complex of a principal ideal domain as an iterated bar construction on an equivariant monoid built out of Tits buildings. We also identify the Koszul dual of a certain equivariant ring assembled out of Steinberg modules.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1628

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

Institutions: Purdue University West Lafayette, University of Oklahoma, University of Michigan

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, European Commission, National Research Foundation, Danmarks Grundforskningsfond