Let $F$ be a number field. The classical class field theory gives an isomorphism between the ideal class group $Cl(F)$ and $\mathrm{Gal}(H/F)$, where $H$ is the Hilbert class field (maximal unramified abelian extension) of $F$. Recall that $Cl(F)$ is the torsion part of $K\_0(\mathcal{O}\_F)$. 
Quillen and Borel determined the abelian group structure of higher K-groups of $\mathcal{O}\_F$. We also knot that they are finitely generated and its size of torsion part is connected with zeta-values like ideal class groups.


My question: do we have a ''class field theory'' describing the (torsion part) of higher K-groups of $\mathcal{O}\_F$ by some ''higher Hilbert class field''?



class field theory for K-groups of number fields
[This](http://mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0419.0428.ocr.pdf) should be what you're looking for. 


