  We consider a second-order parabolic equation in $\bR^{d+1}$ with possibly
unbounded lower order coefficients. All coefficients are assumed to be only
measurable in the time variable and locally H\"older continuous in the space
variables. We show that global Schauder estimates hold even in this case. The
proof introduces a new localization procedure. Our results show that the
constant appearing in the classical Schauder estimates is in fact independent
of the $L_{\infty}$-norms of the lower order coefficients. We also give a proof
of uniqueness which is of independent interest even in the case of bounded
coefficients.
