  We consider the canonical representation of the absolute Galois group of the
rational numbers in the outer automorphism group of the pro-p completion of the
fundamental group of the projective line minus 0,1, and infinity. Deligne has
conjectured that a certain graded Z_p-Lie algebra arising from this
representation becomes a free p-adic Lie algebra on one element in each odd
degree starting with 3 when tensored with the Q_p. We construct good choices of
these elements and use them to examine the structure of the Z_p-Lie algebra. In
particular, we consider how its structure depends upon the regularity of the
prime p by examining a consequence of Greenberg's conjecture in multivariable
Iwasawa theory.
