  Localization methods are ubiquitous in cyclic homology theory, but vary in
detail and are used in different scenarios. In this paper we will elaborate on
a common feature of localization methods in noncommutative geometry, namely
sheafification of the algebra under consideration and reduction of the
computation to the stalks of the sheaf. The novelty of our approach lies in the
methods we use which mainly stem from real instead of complex algebraic
geometry. We will then indicate how this method can be used to determine the
Hochschild homology theory of more complicated algebras out of simpler ones.
