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

Abstract

We compute the $v_1$-periodic $\mathbb{R}$-motivic stable homotopy groups. The main tool is the effective slice spectral sequence. Along the way, we also analyze $\mathbb{C}$-motivic and $\eta$-periodic $v_1$-periodic homotopy from the same perspective.

arXiv comment42 pages, 19 figures

References in corpus (9)

• Motivic and Real Etale Stable Homotopy Theory
• Low dimensional Milnor-Witt stems over R
• C_2-equivariant stable homotopy from real motivic stable homotopy
• The Adams-Novikov spectral sequence and Voevodsky's slice tower
• The eta-inverted R-motivic sphere
• The eta-inverted sphere over the rationals
• The homotopy groups of the η-periodic motivic sphere spectrum
• The $C_2$-effective spectral sequence for $C_2$-equivariant connective real $K$-theory
• The Adams spectral sequence for the image-of-$J$ spectrum