On some Properties of the Nottingham Group

MEMBERS SEMINAR
Topic:On some Properties of the Nottingham Group
Speaker:Mikhail Ershov
Affiliation:IAS
Date:Monday, November 7
Time/Room:4:00pm - 5:00pm/S-101

Let F be a finite field. The Nottingham group N(F) is the group of formal power series \{ t(1+a_1 t + a_2 t^2 + ...): a_i \in F \}or, equivalently, the group of wild automorohisms of the local field F((t)). In spite of such a simple definition, the subgroup structure of the Nottingham group remains rather mysterious. In this talk I will discuss why the Nottingham group behaves in many aspects like algebraic groups over local fields but at the same exhibits certain "very nonlinear" features.