### Relationships between conjectures on the structure of pro-p Galois groups unramified outside p, by Romyar T. Sharifi

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.

Romyar T. Sharifi <sharifi@math.arizona.edu>