A Coalgebra Model for p-adic Homotopy Types

By a theorem of Mandell connected p-complete nilpotent spaces of finite p-type are classified by a natural E_infty-algebra structure on cochains with coefficients in the algebraic closure of the field with p-elements.  
In this talk I will discuss an extension of Mandell's theorem classifying all connected p-complete nilpotent spaces not necessarily of finite p-type by a natural E_infty-coalgebra structure on chains with coefficients in the algebraic closure of the field with p-elements. This project is joint work in progress with Manfred Stelzer.