The Structure of Motivic Homotopy Groups

Bogdan Gheorghe; Daniel C. Isaksen

The Structure of Motivic Homotopy Groups

Algebraic Topology 2015-05-07 v1

Authors: Bogdan Gheorghe , Daniel C. Isaksen

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.

Keywords

motivic homotopy groups stable homotopy groups motivic sphere spectrum 2-completion eta-local region tau-local region classical stable homotopy groups

Cite

@article{arxiv.1505.01476,
  title  = {The Structure of Motivic Homotopy Groups},
  author = {Bogdan Gheorghe and Daniel C. Isaksen},
  journal= {arXiv preprint arXiv:1505.01476},
  year   = {2015}
}

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8 pages, 1 figure

The Structure of Motivic Homotopy Groups

Abstract

Keywords

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