Formal A-modules and the Adams-Novikov spectral sequence

ROOTS OF UNITY AND THE ADAMS-NOVIKOV SPECTRAL SEQUENCE FOR FORMAL yl-MODULES

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...

BP -Theory and the Adams–Novikov Spectral Sequence

The Adams-novikov Spectral Sequence for the Spheres

The Adams spectral sequence has been an important tool in research on the stable homotopy of the spheres. In this note we outline new information about a variant of the Adams sequence which was introduced by Novikov [7]. We develop simplified techniques of computation which allow us to discover vanishing lines and periodicity near the edge of the E2-term, interesting elements in E^'*, and a cou...

On the Adams Spectral Sequence for R-modules

We consider the Adams Spectral Sequence for R-modules based on commutative localized regular quotient ring spectra of a commutative S-algebra R in the sense of Elmendorf, Kriz, Mandell, May and Strickland. The formulation of this spectral sequence is similar to the classical case, and we reduce to algebra involving the cohomology of certain ‘brave new Hopf algebroids’ E ∗ E. In order to work ou...

The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres

These are notes for a five lecture series intended to uncover large-scale phenomena in the homotopy groups of spheres using the Adams-Novikov Spectral Sequence. The lectures were given in Strasbourg, May 7–11, 2007.