$K$-theory of rings of continuous functions
Abstract
We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case reproves the results of Rosenberg, Friedlander-Walker, and Cortinas-Thom. Our consideration in the real case proves two previously unconfirmed claims made by Rosenberg in 1990. The algebraic nature of our methods enables us to deal with the nonarchimedean and noncommutative cases analogously.
Fields of Study & Subjects
Rings
Modules
and Algebras
Advanced Topology and Set Theory
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Cambridge Journal of Mathematics
- Publisher
- International Press of Boston
- Volume
- 14
- Issue
- 2
- Pages
- 243–283
- Publication date
- 1 January 2026
- Language
- EN