The C-motivic Adams-Novikov spectral sequence for topological modular forms

Abstract

We analyze the $C$-motivic (and classical) Adams-Novikov spectral sequence for the $C$-motivic modular forms spectrum mmf (and for the classical topological modular forms spectrum tmf). We primarily use purely algebraic techniques, with a few exceptions. Along the way, we settle a previously unresolved detail about the multiplicative structure of the homotopy groups of tmf.