A family of K(n)-local finite complexes with nice homotopy groups

In monochromatic stable homotopy theory, there are two key parameters, given by the prime and the height. It is known that the situation tends to simplify considerably when the prime is much larger than the height. For example, the Adams-Novikov spectral sequence collapses for all generalized Moore spectra, giving an algebraic description of K(n)-stable homotopy groups. 

I will explain how if one is willing to replace the K(n)-local sphere by its finite Galois extension, the collapse of the Adams-Novikov spectral sequence can always be arranged, at any height and any prime. This gives a family of K(n)-local finite complexes with particularly simple homotopy groups. This talk is based on joint work with David Lee.