  We formulate a theory of doped magnetic semiconductors such as
Ga$_{1-x}$Mn$_x$As which have attracted recent attention for their possible use
in spintronic applications. We solve the theory in the dynamical mean field
approximation to find the magnetic transition temperature $T_c$ as a function
of magnetic coupling strength $J$ and carrier density $n$. We find that $T_c$
is determined by a subtle interplay between carrier density and magnetic
coupling.
