  Let X be a smooth variety over an algebraically closed field of
characteristic p > 0, Z a smooth divisor, and j : U = X\Z --> X the natural
inclusion. An axiomatizing of the properties of a V -filtration on a unit
F-crystal is proposed and is proven to determine a unique filtration. It is
shown that if M is a tame unit F-crystal on U then such a V -filtration along Z
exists on j_*M. The degree zero component of the associated graded module is
proven to be the (unipotent) nearby cycles functor of Grothendieck and Deligne
under the Emerton-Kisin Riemann-Hilbert correspondence. A few applications to
A^1 and gluing are then discussed.
