  This paper concerns our earlier conjecture about the equivalence of a derived
completion construction applied to the representation spectrum of the absolute
Galois group of a geometric field is equivalent to the algebraic K-theory of
the field. We prove that the p-adic version of the derived completion
construction can be interpreted as the K-theory of a certain pro-scheme over an
algebraically closed field contained within the field. In order to make this
construction, we use a special property of absolute Galois groups of geometric
field, namely that of total torsion freeness, and the paper also contains some
poperties of the representation theory of such groups.
