English Translation of Chapter 9 of the book Adams spectral sequence and stable homotopy groups of spheres (In Chinese)

The cohomology of a Hopf algebroid related to the Adams-Novikov spectral sequence for formal ,4-modules is studied in the special case in which A is the ring of integers in the field obtained by adjoining pth roots of unity to Qp , the p-adic numbers. Information about these cohomology groups is used to give new proofs of results about the E2 term of the Adams spectral sequence based on 2-local...

Abstract In this paper, we introduce a four-filtrated version of the May spectral sequence (MSS), from which we study the general properties of the spectral sequence and give a collapse theorem. We also give an efficient method to detect generators of May E1-term E s,t,b,∗ 1 for a given (s, t, b, ∗). As an application, we give a method to prove the non-triviality of some compositions of the kno...

Using the Landweber}Araki theory of Real cobordism and Real-oriented spectra, we de"ne a Real analogue of the Adams}Novikov spectral sequence. This is a new spectral sequence with a potentially calculable E 2 -term. It has versions converging to either the Z/2-equivariant or the non-equivariant stable 2-stems. We also construct a Real analogue of the Miller}Novikov &algebraic' spectral sequence...