The small $x$ nuclear shadowing at DIS

We estimate the perturbative nuclear shadowing in the nuclear structure function $F_2^A(x,Q^2)$, mainly at the kinematic region of HERA using the Glauber-Mueller approach. The contributions of the quark and gluon sectors to the nuclear shadowing are estimated. We predict that the nuclear shadowing corrections are important and that saturation of the ratio $R_1 = F_2^{A}(x,Q^2)/A F^p_2(x,Q^2)$ occurs once the shadowing in the gluon sector is considered.