  We prove Strichartz estimates for the Schroedinger operator $H = -\Delta +
V(t,x)$ with time-periodic complex potentials $V$ belonging to the
scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is
done directly from estimates on the resolvent rather than using dispersive
bounds, as the latter generally require a stronger regularity condition than
what is stated above. In typical fashion, we project onto the continuous
spectrum of the operator and must assume an absence of resonances. Eigenvalues
are permissible at any location in the spectrum, including at threshold
energies, provided that the associated eigenfunction decays sufficiently
rapidly.
