Abstract Goerss-Hopkins theory

Abstract

We present an abstract version of Goerss-Hopkins theory in the setting of a prestable $\infty$-category equipped with a suitable periodicity operator. In the case of the $\infty$-category of synthetic spectra, this yields obstructions to realizing a comodule algebra as a homology of a commutative ring spectrum, recovering the results of Goerss and Hopkins.

37 pages, comments welcome. Edited in response to referee comments and to add Example 8.8 due to Robert Burklund