  We provide a general method to construct local infrared subtraction
counterterms for unresolved radiative contributions to differential cross
sections, to any order in perturbation theory. We start from the factorised
structure of virtual corrections to scattering amplitudes, where soft and
collinear divergences are organised in gauge-invariant matrix elements of
fields and Wilson lines, and we define radiative eikonal form factors and jet
functions which are fully differential in the radiation phase space, and can be
shown to cancel virtual poles upon integration by using completeness relations
and general theorems on the cancellation of infrared singularities. Our method
reproduces known results at NLO and NNLO, and yields substantial
simplifications in the organisation of the subtraction procedure, which will
help in the construction of efficient subtraction algorithms at higher orders.
