  We study the dispersive properties of the linear Schr\"odinger equation with
a time-dependent potential $V(t,x)$. We show that an appropriate integrability
condition in space and time on $V$, i.e. the boundedness of a suitable
$L^{r}_{t}L^{s}_{x}$ norm, is sufficient to prove the full set of Strichartz
estimates. We also construct several counterexamples which show that our
assumptions are optimal, both for local and for global Strichartz estimates, in
the class of large unsigned potentials $V\in L^{r}_tL^{s}_x$.
