The 2-primary Adams-Novikov spectral sequence for C-motivic modularforms

Abstract

The C-motivic modular forms mmf is the C-motivic analog of topological modular forms tmf. ltserves as an approximation to the C-motivic sphere spectrum. We analyze the 2-primary Adams-Novikov spectral seguence for mmf by using algebraic techniques as much as possible. We givecomplete descriptions of the E 2-page, all differentials, the E infty-page, all hidden extensionsby 2, eta, and nu. Our technigues settle an open problem about the multiplicative structure of thehomotopy of tmf proposed by Bruner and Rognes. This is a joint work with Daniel C. lsaksen, HanaJia Kong, Guchuan Li, Heyi Zhu on arXiv:2302.09123. In this talk, l will show some techniques todeduce Adams-Novikov differentials including using the spectrum mmf/tau, comparing the Adamsand the Adams-Novikov spectral sequences, Moss convergence theorem, and hidden extensions.