  Heavy quark production has been very well studied over the last years both
theoretically and experimentally. Theory has been used to study heavy quark
production in $e p$ collisions at HERA, in $pp$ collisions at Tevatron and at
RHIC, in $pA$ and $dA$ collisions at RHIC and in $AA$ collisions at CERN-SPS
and at RHIC. However, to the best of our knowledge, heavy quark production in
$eA$ has received almost no attention. With the possible construction of a high
energy electron-ion collider, updated estimates of heavy quark production are
needed. We address the subject from the perspective of saturation physics and
compute the heavy quark production cross section with the dipole model. We
isolate shadowing and non-linear effects, showing their impact on the charm
structure function and on the transverse momentum spectrum.
