The first stable homotopy groups of motivic spheres

TL;DR

This paper computes the first stable homotopy groups of motivic spheres over fields of characteristic not two, linking them to hermitian and Milnor K-groups through spectral sequence analysis.

Contribution

It provides the first explicit computation of the 1-line of stable homotopy groups of motivic spheres over certain fields, advancing understanding in motivic homotopy theory.

Findings

Explicit description of the 1-line of stable homotopy groups

Connection established between motivic homotopy groups and K-theory

Resolution of convergence and differential questions in the slice spectral sequence

Abstract

We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence.