#### Volume 18, issue 3 (2018)

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The eta-inverted sphere over the rationals

### Glen Matthew Wilson

Algebraic & Geometric Topology 18 (2018) 1857–1881
##### Abstract

We calculate the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map $\eta$ 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 ${\mathbb{F}}_{q}$ of odd characteristic) and the field of rational numbers; the ring structure is also determined.

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##### Keywords
motivic homotopy theory, Adams spectral sequence, stable homotopy groups of spheres
##### Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 18G15, 55Q45, 55T15