Pro-$p$ Extensions of Global Fields and pro-$p$ Groups

Abstract

The meeting Pro-$p$ Extensions of Global Fields and pro-$p$ Groups was organised by Nigel Boston (Madison), John Coates (Cambridge) and Fritz Grunewald (Düsseldorf). As the name of the meeting conveys, a primary aim was to bring together group theorists working in the field of pro-$p$ groups and number theorists interested in pro-$p$ extensions of global fields. The workshop consisted of over $25$ talks, supplemented by informal discussions. Topics included: Galois groups of extensions with restricted ramification, self-similar and automata groups, non-commutative Iwasawa theory, groups acting on rooted trees.

This meeting was well attended with over $50$ participants; more than $30$ of these came from countries other than Germany. The range of topics and the diverse backgrounds of the participants led to a stimulating exchange of recent results, challenging problems and general ideas. The organisers and participants thank the Mathematisches Forschungsinstitut Oberwolfach for providing the setting for this successful workshop. The following extended abstracts appear in the chronological order of the talks; they were collected and edited by Benjamin Klopsch (Düsseldorf).