  Using a local construction from a previous paper, we exhibit a numerical
invariant, the differential Swan conductor, for an isocrystal on a variety over
a perfect field of positive characteristic overconvergent along a boundary
divisor; this leads to an analogous construction for certain p-adic and l-adic
representations of the etale fundamental group of a variety. We then
demonstrate some variational properties of this definition for overconvergent
isocrystals, paying special attention to the case of surfaces.
