Joint IAS/Princeton Arithmetic Geometry Seminar
Algebraic K-theory of Rings of Continuous Functions
Recent interactions between condensed mathematics and K-theory have led us to revisit the topic of (nonconnective) algebraic K-theory of topological algebras. In this talk, among recent developments, I will focus on the ring of continuous functions on a compact Hausdorff space valued in a local field (or a local division ring). This work resolves a previously unconfirmed claim about negative K-theory made by Rosenberg in 1990. The method employed is inspired by the resolution of Weibel's conjecture. The main result provides new counterexamples in K-theory by importing pathology from general topology.