Stochastic equations with time-dependent singular drift

We prove unique weak solvability and Feller property for stochastic differential equations with drift in a large class of time-dependent vector fields. This class contains, in particular, the critical Ladyzhenskaya-Prodi-Serrin class, the weak $L^d$ class as well as some vector fields that are not even in $L_{\mathrm{l}\mathrm{o}\mathrm{c}}^{2+\epsilon }$, $\epsilon >0$.