Algebra/Topology seminar

Speaker: Drew Heard

Title: The E_2-term of the K(n)-local E_n-based Adams spectral sequence

Abstract: Chromatic homotopy theory implies that the stable homotopy groups of a finite p-local spectrum X can be reassembled from the homotopy groups of a certain sequence of localisations with respect to a generalisd cohomology theory known as Morvava K-theory, K(n).  To compute these homotopy groups Devinatz and Hopkins introduced the K(n)-local E_n-based Adams spectral sequence. Under certain restrictive conditions the E_2-term of this spectral sequence can be given as continuous group cohomology. We generalise previous known results by working in a category of L-complete comodules, and showing that the E_2-term can be given, under very mild conditions, by a relative Ext functor in this category. We show how, in certain cases, these can be identified with continuous group cohomology. The talk will start with a gentle introduction to the chromatic approach and relevant background on Morava K theory and Morava E-theory.