The cohomology of $C_2$-equivariant $A(1)$ and the homotopy of $k{o}_{C_2}$

Abstract

We compute the cohomology of the subalgebra $A^{C_2}(1)$ of the $C_2$-equivariant Steenrod algebra $A^{C_2}$. This serves as the input to the $C_2$-equivariant Adams spectral sequence converging to the $RO(C_2)$-graded homotopy groups of an equivariant spectrum $k{o}_{C_2}$. Our approach is to use simpler $\mathbb{C}$-motivic and $\mathbb{R}$-motivic calculations as stepping stones.

57 pages. Final version. To appear in the Tunisian Journal of Mathematics

References in corpus (1)

• Gorenstein duality for Real spectra

Cited by in corpus (5)

• Real motivic and $C_2$-equivariant Mahowald invariants
• The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory
• The reduced ring of the $RO(C_2)$-graded $C_2$-equivariant stable stems
• Galois reconstruction of Artin-Tate $\mathbb{R}$-motivic spectra
• The motivic lambda algebra and motivic Hopf invariant one problem