Joint Princeton University/Rutgers/Institute for Advanced Study

NUMBER THEORY SEMINAR
for 5/6/2003

Helmut Koch
Humboldt University, Berlin

Let p be a prime, K an algebraic number field and S a finite set of places of K.  Then K_S denotes the maximal p-extension unramified outside S.  The Galois group G_S of K_S/K is a pro-p-group with finitely many generators and relations.  Subject of the talk is the finer structure of G_S mostly in the case of K=\mathbb{Q}.  After an historical introdution, we explain recent results of Boston, Leedham-Green, Eick and the speaker.