  We generalize a recent result of Clausen: For a number field with integers O,
we compute the K-theory of locally compact O-modules. For the rational integers
this recovers Clausen's result as a special case. Our method of proof is quite
different: Instead of a homotopy coherent cone construction in infinity
categories, we rely on calculus of fraction type results in the style of
Schlichting. This produces concrete exact category models for certain
quotients, a fact which might be of independent interest. As in Clausen's work,
our computation works for all localizing invariants, not just K-theory.
