  We report a comprehensive study of the complex AC conductivity of thin
effectively 2D amorphous superconducting InO_x films at zero applied field.
Below a temperature scale T_c0 where the superconducting order parameter
amplitude becomes well defined, there is a temperature where both the
generalized superfluid stiffness acquires a frequency dependence and the DC
mangetoresistance becomes linear in field. We associate this with a transition
of the Kosterlitz-Thouless-Berezinskii (KTB) type. At our measurement
frequencies the superfluid stiffness at T_KTB is found to be larger than the
universal value. Although this may be understood with a vortex dielectric
constant of epsilon_v ~ 1.9 within the usual KTB theory, this is a relatively
large value and indicates that such a system may be out of the domain of
applicability of the low-fugacity (low vortex density) KTB treatment. This
opens up the possibility that at least some of the discrepancy from a
non-universal magnitude is intrinsic. Our finite frequency measurements allow
us access to a number of other phenomena concerning the charge dynamics in
superconducting thin films, including an enhanced conductivity near the
amplitude fluctuation temperature T_c0 and a finite dissipation at low
temperature which appears to be a universal aspect of highly disordered
superconducting films.
