  Main theorem of [Buyukboduk, arXiv:0706.0377v1] suggests that it should be
possible to lift the Kolyvagin systems of Stark units constructed in
[Buyukboduk, arXiv:math/0703426v1] to a Kolyvagin system over the cyclotomic
Iwasawa algebra. This is what we prove in this paper. This construction gives
the first example towards a more systematic study of Kolyvagin system theory
over an Iwasawa algebra when the core Selmer rank is greater than one. As a
result of this construction, we reduce the main conjectures of Iwasawa theory
for totally real fields to a statement of local Iwasawa theory. This statement,
however, turns out to be interesting in its own right as it suggests a relation
between solutions to $p$-adic and complex Stark conjectures.
