Work

The zeroth stable homotopy groups of motivic spheres over the integers

Year: 2026

Type: preprint

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 connective Witt theory, as well as an absolute purity result for the η-inverted motivic sphere spectrum, is established over Dedekind domains of mixed characteristic.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.03069

Author: Röndigs, Oliver

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Niedersächsische Ministerium für Wissenschaft und Kultur, Deutsche Forschungsgemeinschaft, Volkswagen Foundation, Division of Mathematical Sciences

Awards: SLMath: Opening Doors to Mathematics, Reinheit in motivischer Homotopietheorie, G4713160749

OpenAlex ID: W7220417310

Cites: 6

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Related to: 10