K-theory of the norm functor
Abstract
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.
Cite
@article{arxiv.math/0701628,
title = {K-theory of the norm functor},
author = {Max Karoubi and Thierry Lambre},
journal= {arXiv preprint arXiv:math/0701628},
year = {2009}
}
Comments
30 pages ; in this new and slightly longer version, we have corrected some minor errors and typos in the previous one. To be published in the Journal of Algebra. See also http://www.math.jussieu.fr/~karoubi/