Geodesic
The wedge family of the cohomology of the $\mathbb{C}$-motivic Steenrod algebra
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 101-117.

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

We describe some regular behavior in the motivic wedge, which is an infinite family in the cohomology $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$ of the $\mathbb{C}$-motivic Steenrod algebra. The key tool is to compare motivic computations to classical computations, to $\mathrm{Ext}_{\mathbf{A}(2)}(\mathbb{M}_2,\mathbb{M}_2)$, or to $h_1$-localization of $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$. We also give two conjectures on the behavior of the families $e_0^tg^k$ and $\Delta h_1 e_0^t g^k$ in $\mathrm{Ext}_{\mathbf{A}}(\mathbb{M}_2,\mathbb{M}_2)$ which raise naturally from the study of the motivic wedge family.
DOI : 10.4310/HHA.2021.v23.n1.a7
Classification : 55S10, 55T15
Keywords: cohomology of the Steenrod algebra, motivic homotopy theory 
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     title = {The wedge family of the cohomology of the $\mathbb{C}$-motivic {Steenrod} algebra},
     journal = {Homology, homotopy, and applications},
     pages = {101--117},
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Hieu Thai. The wedge family of the cohomology of the $\mathbb{C}$-motivic Steenrod algebra. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 101-117. doi : 10.4310/HHA.2021.v23.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a7/

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