Kᵢloc(C), i = 0, 1

الأصل · EN

In this article we compute the local algebraic K-theory, i = 0, 1, of the algebra of complex numbers C endowed with the trivial filtration, i.e. Cμ= C, for any μ∈ N; local algebras and local algebraic Klocᵢ-theory were introduced in TelemanₐrXivᵢV. Theorem 3 states the result. This case corresponds in the simplest case to the Alexander-Spanier local K-theory over the point. This article is part of a comprehensive program aimed at re-stating the index theorem, see TelemanₐrXivᵢII. Other articles in this series are TelemanₐrXivᵢV, TelemanₐrXivᵢ, TelemanₐrXivᵢI.