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

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 𝔽q of odd characteristic) and the field of rational numbers; the ring structure is also determined.

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motivic homotopy theory, Adams spectral sequence, stable homotopy groups of spheres
Mathematical Subject Classification 2010
Primary: 14F42
Secondary: 18G15, 55Q45, 55T15
Received: 30 August 2017
Revised: 26 October 2017
Accepted: 7 November 2017
Published: 3 April 2018
Glen Matthew Wilson
Department of Mathematics
University of Oslo