Splitting in the K-theory localization sequence of number fields
Number Theory
2010-02-25 v2 K-Theory and Homology
Abstract
Let p be a rational prime and let F be a number field. Then, for each i>0, there is a short exact localization sequence for K_{2i}(F). If p is odd or F is nonexceptional, we find necessary and sufficient conditions for this exact sequence to split: these conditions involve coinvariants of twisted p-parts of the p-class groups of certain subfields of the fields F(\mu_{p^n}) for n\in N. We also compare our conditions with the weaker condition WK^{et}_{2i}(F)=0 and give some example.
Cite
@article{arxiv.1002.2936,
title = {Splitting in the K-theory localization sequence of number fields},
author = {Luca Caputo},
journal= {arXiv preprint arXiv:1002.2936},
year = {2010}
}
Comments
18 pages, typos corrected, some explicit computation added, attribution of a theorem rectified (and references changed accordingly)