The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory

Abstract

We construct a $C_2$-equivariant spectral sequence for RO$(C_2)$-graded homotopy groups. The construction is by using the motivic effective slice filtration and the $C_2$-equivariant Betti realization. We apply the spectral sequence to compute the RO$(C_2)$-graded homotopy groups of the completed $C_2$-equivariant connective real $K$-theory spectrum. The computation reproves the $C_2$-equivariant Adams spectral sequence results by Guillou, Hill, Isaksen and Ravenel.

arXiv commentCorrected typos

References in corpus (9)

• Motivic and Real Etale Stable Homotopy Theory
• Slices of hermitian K-theory and Milnor's conjecture on quadratic forms
• The Adams-Novikov spectral sequence and Voevodsky's slice tower
• The Witt group of real algebraic varieties
• Motivic Hopf elements and relations
• A structure theorem for $RO(C_2)$-graded Bredon cohomology
• The cohomology of $C_2$-equivariant $A(1)$ and the homotopy of $k{o}_{C_2}$
• On the Slice Spectral Sequence
• On equivariant and motivic slices

Cited by in corpus (1)

• $\mathbb{R}$-motivic $v_1$-periodic homotopy