Sur la K-theorie du foncteur norme, by Max Karoubi and Thierry Lambre

This is a revised version of the preprint 845. Some minor errors have been corrected. To be published in the Journal of Algebra.

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) 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 for some of them with different methods.


Max Karoubi <karoubi@math.jussieu.fr>
Thierry Lambre <thierry.lambre@math.univ-bpclermont.fr>