### Higher wild kernels and divisibility in the K-theory of number fields, by Charles A. Weibel

The higher wild kernels are finite subgroups of the even K-groups
of a number field F, generalizing Tate's wild kernel for K_{2}.
Each wild kernel contains the subgroup of divisible elements,
as a subgroup of index at most two. We determine when they are equal,
i.e., when the wild kernel is divisible in K-theory.

Here is a special case of interest.
Although the map from Milnor K^{M}_{4}(F) to K_{4}(F)
can be nonzero, the image of this map consists of divisible elements.
In particular, these elements cannot be detected by finite quotients
of K_{4}(F).

This paper has appeared in
*J. Pure Applied Algebra* 206 (2006), 222-244.

Charles A. Weibel <weibel@math.rutgers.edu>