The E2-term of the K(n)-local En-Adams spectral sequence

Let E=EnE=En be Morava E-theory of height n. In [8] Devinatz and Hopkins introduced the K(n)K(n)-local EnEn-Adams spectral sequence and showed that, under certain conditions, the E2E2-term of this spectral sequence can be identified with continuous group cohomology. We work with the category of L  -complete E⁎∨E-comodules, and show that in a number of cases the E2E2-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.