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arXiv · 1906.11670

The homotopy groups of the {\eta}-periodic motivic sphere spectrum

Kyle Ormsby·Oliver Röndigs
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Abstract

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

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Kyle Ormsby, Oliver Röndigs. 2019-06-27. The homotopy groups of the {\eta}-periodic motivic sphere spectrum. https://doi.org/10.2140/pjm.2020.306.679

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