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 K2. 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 KM4(F) to K4(F) can be nonzero, the image of this map consists of divisible elements. In particular, these elements cannot be detected by finite quotients of K4(F).

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

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