The K-theory of a functor may be viewed as a relative version of the K-theory
of a ring. In the case of a Galois extension of a number field F/L with rings
of integers A/B respectively, this K-theory of the "norm functor" is an
extension of a subgroup of the ideal class group Cl(A) of F by the 0-Tate
cohomology group with coefficients in A*. The Mayer-Vietoris exact sequence
enables us to describe quite explicitly this extension which is related to the
coinvariants of Cl(A) under the action of the Galois group. We apply these
ideas to find results in Number Theory, which are known to be true for some of
them, with different methods.
The current version has a gap in lemma 6.3.