The $E_2$-term of the $K(n)$-local $E_n$-Adams spectral sequence

Abstract

Let $E=E_n$ be Morava $E$-theory of height $n$. In previous work Devinatz and Hopkins introduced the $K(n)$-local $E_n$-Adams spectral sequence and showed that, under certain conditions, the $E_2$-term of this spectral sequence can be identified with continuous group cohomology. We work with the category of $L$-complete $E_{\ast }E$-comodules, and show that in a number of cases the $E_2$-term of the above spectral sequence can be computed by a relative Ext group in this category. We give suitable conditions for when we can identify this Ext group with continuous group cohomology.

23 pages. Substantially revised and reorganized. Final version, to appear in Topology and its Applications

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• Morava K-theory and Filtrations by Powers
• Algebraicity in monochromatic homotopy theory
• The inverse limit topology and profinite descent on Picard groups in $K(n)$-local homotopy theory