The wedge family of the cohomology of the $\mathbb{C}$-motivic Steenrod algebra

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.

Keywords

cohomology of the Steenrod algebra, motivic homotopy theory

2010 Mathematics Subject Classification

55S10, 55T15

Full Text (PDF format)

Received 5 November 2019

Received revised 20 February 2020

Accepted 3 March 2020

Published 26 August 2020