## Algebraic & Geometric Topology

### The eta-inverted sphere over the rationals

Glen Matthew Wilson

#### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1524708108

Digital Object Identifier
doi:10.2140/agt.2018.18.1857

Mathematical Reviews number (MathSciNet)
MR3784021

Zentralblatt MATH identifier
06866415

#### Citation

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. https://projecteuclid.org/euclid.agt/1524708108

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