# Reconstructing rational stable motivic homotopy theory

## TL;DR

This paper reconstructs rational stable motivic homotopy theory over certain fields using finite Milnor-Witt correspondences, building on recent computations and established theorems to provide a new perspective.

## Contribution

It introduces a novel reconstruction of rational stable motivic homotopy theory via finite Milnor-Witt correspondences, connecting recent computational results with classical theorems.

## Key findings

- Reconstruction of rational stable motivic homotopy theory from finite Milnor-Witt correspondences.
- Utilization of recent computations of the rational minus part of SH(k).
- Application of theorems by Cisinski-Deglise and Roendigs-Ostvaer to this context.

## Abstract

Using a recent computation of the rational minus part of $SH(k)$ by Ananyevskiy-Levine-Panin, a theorem of Cisinski-Deglise and a version of the Roendigs-Ostvaer theorem, rational stable motivic homotopy theory over an infinite perfect field of characteristic different from 2 is recovered in this paper from finite Milnor-Witt correspondences in the sense of Calmes-Fasel.