Algebraic & Geometric Topology

The eta-inverted sphere over the rationals

Glen Matthew Wilson

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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 p and the finite fields F q of odd characteristic) and the field of rational numbers; the ring structure is also determined.

Article information

Algebr. Geom. Topol., Volume 18, Number 3 (2018), 1857-1881.

Received: 30 August 2017
Revised: 26 October 2017
Accepted: 7 November 2017
First available in Project Euclid: 26 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F42: Motivic cohomology; motivic homotopy theory [See also 19E15]
Secondary: 18G15: Ext and Tor, generalizations, Künneth formula [See also 55U25] 55Q45: Stable homotopy of spheres 55T15: Adams spectral sequences

motivic homotopy theory Adams spectral sequence stable homotopy groups of spheres


Wilson, Glen Matthew. The eta-inverted sphere over the rationals. Algebr. Geom. Topol. 18 (2018), no. 3, 1857--1881. doi:10.2140/agt.2018.18.1857.

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