Splitting in the K-theory localization sequence of number fields

Let p be a rational prime and let F be a number field. Then, for each i≥1, Quillen’s K-theory group K2i(F) is a torsion abelian group, containing the finite subgroup K2i(OF), where OF is the ring of integers of F. If p is odd or F is nonexceptional or i is even, we give necessary and sufficient conditions for the p-primary component of K2i(OF)⊂K2i(F) to split. Our conditions involve coinvariants of twisted p-parts of the p-class groups of certain subfields of the fields F(μpn) for n∈N. We also compare our conditions with the weaker condition and give some examples.