  Fix a prime number ell. In this paper we develop the theory of relative
pro-ell completion of discrete and profinite groups -- a natural generalization
of the classical notion of pro-ell completion -- and show that the pro-ell
completion of the Torelli group does not inject into the relative pro-ell
completion of the corresponding mapping class group when the genus is at least
3. As an application, we prove that when g > 2, the action of the pro-ell
completion of the Torelli group T_{g,1} on the pro-ell fundamental group of a
pointed genus g surface is not faithful.
  The choice of a first-order deformation of a maximally degenerate stable
curve of genus g determines an action of the absolute Galois group G_Q on the
relative pro-ell completion of the corresponding mapping class group. We prove
that for all g all such representations are unramified at all primes \neq ell
when the first order deformation is suitably chosen. This proof was
communicated to us by Mochizuki and Tamagawa.
