  We analyze here the behavior near the 2D insulator-superconductor quantum
critical point in the presence of a perpendicular magnetic field. We show that
with increasing field $H$, the quantum disordered and quantum critical regimes,
in which vortex degrees of freedom are suppressed, crossover to a new
magnetically activated (MA) regime, where the correlation length $\xi \sim
1/\sqrt{H}$. In this regime, we show that the conductivity decreases
monotonically as opposed to the anticipated saturation predicted from
hyperuniversality arguments. This discrepancy arises from the lack of
commutativity of the frequency and temperature tending to zero limits of the
conductivity. In the low-field regime such that $\sqrt{H}\ll\Delta$, and in the
absence of Ohmic dissipation, where $\Delta$ is a measure of the distance from
the quantum critical point, the resistivity saturates to the Bose metal value
found previously for Cooper pairs lacking phase coherence.
