Algèbre et géométrie

Shelah's conjecture predicts that any infinite NIP field iseither separably closed, real closed or admits a non-trivial henselianvaluation. Recently, Johnson proved that Shelah's conjecture holds forfields of finite dp-rank, also known as dp-finite fields. The aim of these two talks is to give an introduction to dp-rank in some algebraic structures and an overview of Johnson's work.In the first talk, we define dp-rank (which is a notion of rank in NIP theories) and give examples of dp-finite structures. In particular, we discuss the dp-rank of ordered abelian groups and use […]