The $E_2$-term of the Adams spectral sequence for $\mathbf{Y}$ may be described in terms its cohomology $E^\ast \mathbf{Y}$, together with action primary operations \mathbf{E}$ on it, ring spectra such as $\mathbf{E} = \mathbf{H}\mathbb{F}_p$. We show how higher can similarly order truncated $\mathbf{E}$-mapping algebra $\; - \;$ that is truncations function $\operatorname{Fun}(\mathbf{Y}, \mat...

One can use next the globalization machinery developed in [S-F] to get a similar looking spectral sequence for any smooth scheme of finite type over a field. Moreover, it’s not hard to see that the resulting spectral sequence coincides with the one constructed in [F-S]. What is nice, however, with this approach is that it avoids completely the use of the paper of Bloch and Lichtenbaum [B-L], wh...

For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations. Bredon [1] introduced what is now called Bredon cohomology, with the purpose of developing obstruction theory in the context of ...

In this article I consider the convergence of the Eilenberg– Moore spectral sequence for Morava K-theory. This spectral sequence can be constructed by applying Morava K-theory to D. L. Rector’s geometric cobar construction of the Eilenberg–Moore spectral sequence. I have shown that the Eilenberg–Moore spectral sequence for Morava Ktheory converges if the Eilenberg–Moore spectral sequence for or...