$K$-theory of rings of continuous functions

Autor:	Aoki, Ko
Rok vydání:	2024
Předmět:	Mathematics - K-Theory and Homology Mathematics - Commutative Algebra Mathematics - Algebraic Geometry Mathematics - General Topology
Druh dokumentu:	Working Paper
Popis:	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 Corti\~nas--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. Comment: 25 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.05257 Zobrazit plný text záznamu View this record from Arxiv