Operations and co-operations in Morava $E$-theory

Mark Hovey

Wesleyan University 
mhovey@wesleyan.edu 

In this paper, we revisit the calculations of the operations and
co-operations in Morava E-theory.  Recall that the co-operations are the
continuous functions from a profinite group G that is a version of the
Morava stabilizer group to E_*.  The operations are the completed
twisted group ring E_*[[G]].  

These results have appeared in the literature before.  The advantage of
this paper is that it is self-contained, works out all the details that
are usually skipped over, and uses a new approach, not directly
dependent on Morava's Annals paper on comodules, that the author finds
fairly simple and elegant.  Most of all, though, the author wrote this
paper because he was unable to understand the proofs in the
literature. He hopes it will be useful for people in the same unhappy
situation.