Algebraic Ktheory of Rings of Continuous Functions
Algebraic Ktheory of Rings of Continuous Functions

Ko Aoki, MPIM Bonn
IAS  Simonyi Hall Seminar Room SH101
Recent interactions between condensed mathematics and Ktheory have led us to revisit the topic of (nonconnective) algebraic Ktheory 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 Ktheory made by Rosenberg in 1990. The method employed is inspired by the resolution of Weibel's conjecture. The main result provides new counterexamples in Ktheory by importing pathology from general topology.