The eta-inverted sphere over the rationals

Wilson, Glen

doi:10.2140/agt.2018.18.1857

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The eta-inverted sphere over the rationals

Glen Matthew Wilson

Algebraic & Geometric Topology 18 (2018) 1857–1881

DOI: 10.2140/agt.2018.18.1857

Abstract

We calculate the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map $η$ over fields of cohomological dimension at most $2$ with characteristic different from $2$ (this includes the $p$ –adic fields $ℚ_{p}$ and the finite fields $𝔽_{q}$ of odd characteristic) and the field of rational numbers; the ring structure is also determined.

Keywords

motivic homotopy theory, Adams spectral sequence, stable homotopy groups of spheres

Mathematical Subject Classification 2010

Primary: 14F42

Secondary: 18G15, 55Q45, 55T15

References

Publication

Received: 30 August 2017

Revised: 26 October 2017

Accepted: 7 November 2017

Published: 3 April 2018

Authors

Glen Matthew Wilson
Department of Mathematics University of Oslo Oslo Norway

Volume 18, issue 3 (2018)