  This manuscript is the outcome of the subgroup ``PDFs, shadowing and $pA$
collisions'' from the CERN workshop ``Hard Probes in Heavy Ion Collisions at
the LHC''. In addition to the experimental parameters for $pA$ collisions at
the LHC, the issues discussed are factorization in nuclear collisions, nuclear
parton distributions (nPDFs), hard probes as the benchmark tests of
factorization in $pA$ collisions at the LHC, and semi-hard probes as
observables with potentially large nuclear effects. Also, novel QCD phenomena
in $pA$ collisions at the LHC are considered. The importance of the $pA$
program at the LHC is emphasized.
