  Perturbative QCD is the appropriate tool to describe many important
properties of the inclusive observables measured at electron-proton (or ion)
colliders, such as the energy dependence of the total cross sections in
well-chosen kinematical regions. This is because the electron may effectively
be replaced by its cloud of photons, whose virtualities provide a hard scale
that enables perturbative expansions.
  At hadron colliders instead, there is no hard scale in the initial state.
Therefore, the observables one may compute perturbatively involve the
production of jets, and thus belong to a quite different class of observables.
  However, it turns out that there is a formal relation between production
processes and total cross sections, enabling one to apply calculations of the
latter to the former. We review this relation, and present our recent proof
that it holds at next-to-leading order (in the BFKL sense).
