Samuel WUETHRICH

I-adic towers in topology

Abstract

Assume that T -> F is a map of ring spectra which induces a surjection on homotopy groups with kernel I and assume that I is generated by a T_*-regular sequence. An I-adic tower consists of a sequence of T-module spectra which realizes the I-adic filtration of T_* on homotopy groups and which has the property that the homotopy fibres of two subsequent spectra split into wedges of suspensions of F. Such a tower gives rise to a Higher Bockstein spectral sequence.

I-adic towers were first constructed for the case where T is completed Johnson-Wilson theory E(n)^ and F is Morava-K-theory K(n) for some prime p by Baker and Wuergler in 1989. More recently, Baker and Lazarev (2001) have constructed I-adic towers under the assumption that T is E-infinity.

The aim of my PhD was to obtain a conceptual understanding of the nature of I-adic towers. It turns out that there is a characterization of algebraic I-adic towers in the derived setting which indicates how to construct topological I-adic towers under rather weak assumptions.

In my talk, I will explain how I-adic towers can be constructed as Adams resolutions in an appropriate sense and discuss the Higher Bockstein spectral sequences derived from such towers.

18 March 2005