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arXiv · 2610.03069

The zeroth stable homotopy groups of motivic spheres over the integers

Oliver Röndigs
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Abstract

The main result determines the zeroth integral Milnor-Witt stem of the motivic sphere spectrum in the Morel-Voevodsky motivic stable homotopy category of the integers. The component in weight zero is the Grothendieck-Witt ring of nondegenerate symmetric bilinear forms over the integers. Along the way, cellularity of various motivic spectra, including the integral motivic Eilenberg-MacLane spectrum, is established over arbitrary fields, as well as an absolute purity result for the η-inverted motivic sphere spectrum over Dedekind domains of mixed characteristic.

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Oliver Röndigs. 2026-10-02. The zeroth stable homotopy groups of motivic spheres over the integers. https://arxiv.org/abs/2610.03069

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