A Note on the Main Conjecture over Q

Abstract

In this note we show how the main conjecture of the Iwasawa theory over Q has a natural place in the context of the Galois representation of the Galois group $Gal(\bar{Q}/Q)$ on the etale pro-p fundamental group of the projective line minus three points. However we still need to assume the Vandiver conjecture to get a proof of the main conjecture in this context.