  In this paper we present a comprehensive study of inclusive hadron production
in DIS at low $x$. Properties of the hadron spectrum are different in different
kinematic regions formed by three relevant momentum scales: photon virtuality
$Q^2$, hadron transverse momentum $k_T$ and the saturation momentum $Q_s(x)$.
We investigate each kinematic region and derive the corresponding asymptotic
formulas for the cross section at the leading logarithmic order. We also
analyze the next-leading-order (NLO) corrections to the BFKL kernel that are
responsible for the momentum conservation. In particular, we establish the
asymptotic behavior of the forward elastic dipole--nucleus scattering amplitude
at high energies deeply in the saturation regime and a modification of the
pomeron intercept. We study the nuclear effect on the inclusive cross section
using the nuclear modification factor and its logarithmic derivative. We argue
that the later is proportional to the difference between the anomalous
dimension of the gluon distribution in nucleus and in proton and thus is a
direct measure of the coherence effects. To augment our arguments and present
quantitative results we performed numerical calculations in the kinematic
region that may be accessible by the future DIS experiments.
