The homotopy groups of the η-periodic motivic sphere spectrum

We compute the homotopy groups of the $η$ -periodic motivic sphere spectrum over a field $k$ of finite cohomological dimension with characteristic not $2$ and in which $- 1$ is a sum of four squares. We also study the general characteristic $0$ case and show that the $α_{1}$ -periodic slice spectral sequence over $ℚ$ determines the $α_{1}$ -periodic slice spectral sequence over all extensions $k ∕ ℚ$ . This leads to a speculation on the role of a “connective Witt-theoretic $J$ -spectrum” in $η$ -periodic motivic homotopy theory.

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Keywords

motivic homotopy theory, stable motivic homotopy sheaves, slice spectral sequence

Mathematical Subject Classification 2010

Primary: 14F42

Secondary: 55Q45

Milestones

Received: 19 September 2019

Revised: 10 January 2020

Accepted: 19 January 2020

Published: 13 July 2020

Authors

Kyle Ormsby
Department of Mathematics Reed College Portland, OR United States

Oliver Röndigs
Institut für Mathematik Universität Osnabrück Osnabrück Germany

Vol. 306, No. 2, 2020

Kyle Ormsby and Oliver Röndigs

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors