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>