  We study transport of interacting electrons in a low-dimensional disordered
system at low temperature $T$. In view of localization by disorder, the
conductivity $\sigma(T)$ may only be non-zero due to electron-electron
scattering. For weak interactions, the weak-localization regime crosses over
with lowering $T$ into a dephasing-induced "power-law hopping". As $T$ is
further decreased, the Anderson localization in Fock space crucially affects
$\sigma(T)$, inducing a transition at $T=T_c$, so that $\sigma(T<T_c)=0$. The
critical behavior of $\sigma(T)$ above $T_c$ is $\ln\sigma(T)\propto -
(T-T_c)^{-1/2}$. The mechanism of transport in the critical regime is
many-particle transitions between distant states in Fock space.
