  We produce a canonical filtration for locally free sheaves on an open p-adic
annulus equipped with a Frobenius structure. Using this filtration, we deduce a
conjecture of Crew on p-adic differential equations, analogous to
Grothendieck's local monodromy theorem (also a consequence of results of Andre
and of Mebkhout). Namely, given a finite locally free sheaf on an open p-adic
annulus with a connection and a compatible Frobenius structure, the
corresponding module admits a basis over a finite cover of the annulus on which
the connection acts via a nilpotent matrix.
  Note: this preprint improves on results from our previous preprints
math.AG/0102173, math.AG/0105244, math.AG/0106192, math.AG/0106193 but does not
explicitly invoke any results from these preprints.
