Let p be a rational prime, and let X be a connected finite graph. In this
article we study voltage covers X∞ of X attached to a voltage
assignment α which takes values in some uniform p-adic Lie group
G. We formulate and prove an Iwasawa main conjecture for the projective limit
of the Picard groups Pic(Xn) of the intermediate voltage covers
Xn, n∈N, and we prove one inclusion of a main conjecture
for the projective limit of the Jacobians J(Xn).
Moreover, we study the MH(G)-property of
Zp[[G]]-modules and prove a necessary condition for this property
which involves the μ-invariants of Zp-subcovers Y⊆X∞ of X. If the dimension of G is equal to 2, then this condition
is also sufficient.Comment: 29 page