  The sharp range of Sobolev spaces is determined in which the Cauchy problem
for the classical Zakharov system is well-posed, which includes existence of
solutions, uniqueness, persistence of initial regularity, and real-analytic
dependence on the initial data. In addition, under a condition on the data for
the Schr\"odinger equation at the lowest admissible regularity, global
well-posedness and scattering is proved. The results cover energy-critical and
energy-supercritical dimensions $d \geqslant 4$.
