Gauge PDEs on spaces with asymptotic boundaries

I plan to discuss a general setup for studying the boundary structure of gauge fields on spaces with asymptotic boundaries. The main example of this situation is asymptotically-anti-de-Sitter (AdS) or flat gravity and (optionally) gauge fields living on such a background. A suitable tool to study systems of this sort  in a geometrical way is the so-called gauge PDE on spaces with (asymptotic) boundaries. When applied to the case of asymptotically-AdS gravity this gives the generalization of the familiar Fefferman-Graham construction that also takes the subleading boundary value into account. When additional (gauge) fields are present this generalizes the known gauge PDE approach to boundary values of AdS gauge fields. An interesting feature is that the gauge PDE induced on the boundary is itself a fibre bundle of gauge PDEs (also known as gauge PDE over background), where the base describes the leading (conformal geometry in the case of gravity) while the fiber correspond to the subleading (conserved currents).