Geodesic
Mapping algebras and the Adams spectral sequence
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 219-242.

Voir la notice de l'article provenant de la source International Press of Boston

For a suitable ring spectrum, such as $\mathbf{E}=\mathbf{H}\mathbb{F}_p$, the $E_2$-term of the $\mathbf{E}$-based Adams spectral sequence for a spectrum $\mathbf{Y}$ may be described in terms of its cohomology $E^{\ast}\mathbf{Y}$, together with the action of the primary operations $E^{\ast}\mathbf{E}$ on it. We show how the higher terms of the spectral sequence can be similarly described in terms of the higher order truncated $\mathbf{E}$-mapping algebra for $\mathbf{Y}$ — that is, truncations of the function spectra $\operatorname{Fun}(\mathbf{Y},\mathbf{M})$ for various $\mathbf{E}$-modules $\mathbf{M}$, equipped with the action of $\operatorname{Fun}(\mathbf{M},\mathbf{M}^\prime)$ on them.
DOI : 10.4310/HHA.2021.v23.n1.a12
Classification : 55T15, 55P42, 55U35
Keywords: spectral sequence, truncation, differentials, cosimplicial resolution, mapping algebra 
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David Blanc; Surojit Ghosh. Mapping algebras and the Adams spectral sequence. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 219-242. doi : 10.4310/HHA.2021.v23.n1.a12. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a12/

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