The Structure of Motivic Homotopy Groups

Abstract

We study the stable motivic homotopy groups ${\pi }_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an $\eta$-local region that is entirely known, a $\tau$-local region that is identical to classical stable homotopy groups, and a region that is not well-understood.

8 pages, 1 figure

References in corpus (1)

• The motivic Adams vanishing line of slope 1/2

Cited by in corpus (1)

• Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf{C}$