Pic(E-Z/4) and Tools to Compute It

In this talk, we describe tools to compute the Picard group of the category of E-G-module spectra where E is Morava E-theory at n=p=2 and G is a finite cyclic subgroup of the Morava stabilizer of order 4. We discuss two tools: 1) A group homomorphism from RO(G) to Pic(E-G) and methods for computing it. 2) The Picard Spectral sequence and some of its equivariant properties. This work is joint with Irina Bobkova, Mike Hill and Vesna Stojanoska