Mild pro-p-Galois groups of algebraic number fields

• Applicant: Dr. Jochen Gärtner
• Subject Area: Mathematics
• Term: from 2012 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 231696112

This research project aims at further developing the theory of mild pro-p-groups as introduced by John Labute as well as studying their applications to duality properties of extensions of algebraic number fields with restricted ramification. The central object is given by the Galois group G_S(p) of the maximal p-extensions of an algebraic number field unramified outside a finite set of places S in the tame case. It is proposed to investigate group theoretical properties of mild pro-p-groups, in particular their relation to higher order Massey products. Furthermore, the objective is to give arithmetic realizations of these groups.The stay at McGill University, Montreal, Canada would provide the opportunity of a collaboration with Professor John Labute.The goals of the research project are the following:1) Give a description of higher order Massey products and Milnor invariants of pro-p-groups of the form G_S(p) in terms of Galois representations and construct explicit examples of mild pro-p-groups with arbitrary Zassenhaus invariant2) Study FAB pro-p-groups, give a purely algebraic or group theoretical description of non-analytic FAB-groups using properties of their associated graded Lie algebras, study applications to FAB-extensions of algebraic number fields3) Give an answer of Serre's question about the classification of one-relator pro-p-groups of cohomological dimension greater than 2 as quotients of free groups by p-th powers

• DFG Programme: Research Fellowships
• International Connection: Canada
• Host: Professor Dr. John R. Labute