  This paper seeks to prove the bijectivity of the "Nash mapping" from the set
of irreducible components of the scheme parametrizing analytic arcs on an
algebraic surface $X$ whose origin is a singular point, into the set of
irreducible components of the exceptional locus of a minimal desingularization
$X'$ of $X$ when the base field has positive characteristic. The idea is to
view the surface as a specialization of another defined over a field of
characteristic zero. A number of related results are proved. Among them, the
construction of a scheme of arcs for a suitable one parameter family of
surfaces which, by using a theorem of M. Artin on lifting of normal surface
singularities to characteristic zero, seems a reasonable candidate to be the
desired tool. But there are some points, necessary for a complete proof, which
are not verified yet.
