For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and duality, are shown to lift to the category of modules over the associated Steenrod algebra. The dependence on the dimension functions of the representations i...

We present a descent style, Bockstein spectral sequence computing Ext over the motivic Steenrod algebra over R and related sub-Hopf algebras. We demonstrate the workings of this spectral sequence in several examples, providing motivic analogues to the classical computations related to BP 〈n〉 and ko.

In this paper we prove the existence of global nilpotence and global torsion bounds for the cohomology of any finite Hopf subalgebra of the Steenrod algebra for the prime 2. An explicit formula for computing such bounds is then obtained. This is used to compute bounds for H* (sán ) fer n < 6 .

We show that the class of p-complete connective spectra with finitely presented cohomology over the Steenrod algebra admits a duality theory related to Brown-Comenetz duality. This construction also produces a full-plane version of the classical Adams spectral sequence for such spectra, which converges to the homotopy groups of a “finite” localization.