On the May spectral sequence at the prime 2

We make a conjecture about the whole E-2 page of the May spectral sequence in terms of generators and relations and we prove it in a subalgebra which covers a large range of dimensions. We show that the E-2 page plays a universal role in the study of Massey products in commutative DGAs. We conjecture that the E-2 page is nilpotent free and also prove it in this subalgebra. We compute all the d(2 )differentials of the generators in the conjecture and construct maps of spectral sequences which allow us to explore Adams vanishing line theorem to compute differentials in the May spectral sequence. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we make a conjecture about the whole E-2 page of the May spectral sequence and prove it in a subalgebra. Our study shows that the E-2 page plays a crucial role in the study of Massey products in commutative DGAs.