$K_i^{loc}(\mathbb{C})$, $i=0,1$

Abstract

In this article we compute the {\em local algebraic $K$-theory}, $i=0,1$, of the algebra of complex numbers $\mathbb{C}$ endowed with the trivial filtration, i.e. ${\mathbb{C}}_{\mu }=\mathbb{C}$, for any $\mu \in \mathbb{N}$; {\em local algebras} and {\em local} algebraic $K_i^{loc}$-theory were introduced in \cite{Teleman_arXiv_IV}. \par Theorem 3 states the result. \par This case corresponds in the simplest case to the Alexander-Spanier {\em local $K$-theory} over the point. \par This article is part of a comprehensive program aimed at re-stating the index theorem, see \cite{Teleman_arXiv_III}. Other articles in this series are \cite{Teleman_arXiv_IV}, \cite{Teleman_arXiv_I}, \cite{Teleman_arXiv_II}.

arXiv comment10 pages

References in corpus (2)

• $Loca{l}^3$ Index Theorem
• Local Algebraic K-Theory

Cited by in corpus (1)

• Noncommutative Topology and Prospects in Index Theory