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...

We construct Quillen type spectral sequences in homology and rational homotopy for coobration sequences which are Eckmann-Hilton dual to analogous ones for bration sequences. These spectral sequences are constructed by direct ltrations of the Adams cobar construction. We also prove various collapsing theorems generalizing results of Clark and Smith in the case of a wedge of 1-connected nicely p...

where pg « ƒ and p is a fibration with fiber F. Suppose that X is a CW-complex of dimension ^2conn(/ ) and conn (F) è l (conn = connectivity). Let [X, Y]B be the set of homotopy classes of pointed maps over f(H : X XI~*Y is a homotopy over ƒ if pHt—f for each / £ / ) . Becker proved in [2], [3] that under these hypotheses [X, Y]B can be given an abelian group structure with [g] as zero element....

Abstract We establish motivic versions of the theorems Lin and Gunawardena, thereby confirming Segal conjecture for algebraic group th roots unity, where is any prime. To achieve this we develop Singer constructions associated to symmetric , introduce a delayed limit Adams spectral sequence.

A spectral sequence which may be regarded as an 'Adams spectral sequence over a fixed space 2?' has been constructed by J. F. McClendon [6] and J.-P. Meyer [8]. This note describes a generalization in which there is no need for any orientability assumptions. The construction is carried out in a suitable stable category, which may be of independent interest. An application to the enumeration of ...

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

It is shown that the ghost kernel for certain equivariant stable cohomotopy groups of projective spaces is non-trivial. The proof is based on the Borel cohomology Adams spectral sequence and the calculations with the Steenrod algebra afforded by it.