  The aim of this article is to introduce Vogel's localization theorem for
classes of D-complexes: this generalization of Waldhausen's localization
theorem is especially useful and powerful in that it gives an explicit and
computable description of the local objects. Next we present an excision
theorem for transverse classes. Finally, we apply these methods to deduce
partial results on Vogel's [Conjecture] on a regular ring R (cf [Bih01]).
