Multiplicative 2-cocycles at the prime 2

Using a previous classification result on symmetric additive 2-cocycles, we collect a variety of facts about the Lubin–Tate cohomology of certain formal groups to produce a presentation of the 2-primary component of the scheme of symmetric multiplicative 2-cocycles. This scheme classifies certain kinds of highly symmetric multiextensions, generalizing those studied by Mumford or Breen. A low-order version of this computation has previously found application in homotopy theory through the σ-orientation of Ando, Hopkins, and Strickland, and the complete computation is reflective of certain structures found in the homotopy type of connective K-theory.