Groupoid homology and K-theory for algebraic actions from number theory
Abstract
We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homology of the topological full groups associated with rings of algebraic integers, and we use our groupoid homology calculation to compute the K-theory for ring C*-algebras of rings of algebraic integers, recovering the results of Cuntz and Li and of Li and Lück without using Cuntz-Li duality. Moreover, we compute the K-theory for C*-algebras attached to integral dynamics, resolving the conjecture by Barlak, Omland, and Stammeier in full generality.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
History and Theory of Mathematics
Publication details
- Journal / source
- Journal of Functional Analysis
- Publisher
- Elsevier BV
- Volume
- 291
- Issue
- 9
- Pages
- 111607–111607
- Publication date
- 12 June 2026
- Language
- EN