Topological models for stable motivic invariants of regular number rings

TL;DR

This paper connects stable motivic invariants of regular number rings to topological data from complex, real, and finite fields, extending foundational identifications in motivic homotopy theory.

Contribution

It introduces a method to express motivic invariants via topological data and extends Morel's identification to more general base schemes.

Findings

Expressed motivic invariants in terms of topological data

Extended Morel's identification to deeper base schemes

Provided new tools for motivic homotopy theory

Abstract

For an infinity of number rings we express stable motivic invariants in terms of topological data determined by the complex numbers, the real numbers, and finite fields. We use this to extend Morel's identification of the endomorphism ring of the motivic sphere with the Grothendieck-Witt ring of quadratic forms to deeper base schemes.