Splitting in the K-theory localization sequence of number fields

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.