BIMSA > BIMSA Topology Seminar The 2-primary Adams-Novikov spectral sequence for C-motivic modular forms
The 2-primary Adams-Novikov spectral sequence for C-motivic modular forms
Organizers
Matthew Burfitt , Jing Yan Li , Jie Wu , Jia Wei Zhou
Speaker
Yang Yang Ruan
Time
Thursday, March 14, 2024 2:20 PM - 4:00 PM
Venue
A3-4-101
Online
Zoom 928 682 9093 (BIMSA)
Abstract
The C-motivic modular forms mmf is the C-motivic analog of topological modular forms tmf. It serves as an approximation to the C-motivic sphere spectrum. We analyze the 2-primary Adams-Novikov spectral sequence for mmf by using “algebraic techniques” as much as possible. We give complete descriptions of the E_2-page，all differentials，the E_infty-page，all hidden extensions by 2, eta, and nu. Our techniques settle an open problem about the multiplicative structure of the homotopy of tmf proposed by Bruner and Rognes. This is a joint work with Daniel C. Isaksen, Hana Jia Kong, Guchuan Li, Heyi Zhu on arXiv:2302.09123. In this talk, I will show some techniques to deduce Adams-Novikov differentials including using the spectrum mmf/tau, comparing the Adams and the Adams-Novikov spectral sequences, Moss convergence theorem, and hidden extensions.