Motivic stable homotopy groups

TL;DR

This paper surveys the current state of computations in motivic stable homotopy groups over different fields, highlighting key spectral sequence tools and outlining future research directions.

Contribution

It provides a comprehensive overview of computational methods and results in motivic stable homotopy theory, emphasizing spectral sequence techniques and future projects.

Findings

Summarizes known computations of motivic stable homotopy groups.

Highlights the use of spectral sequences like Adams and slice spectral sequences.

Outlines future research projects in the field.

Abstract

We survey computations of stable motivic homotopy groups over various fields. The main tools are the motivic Adams spectral sequence, the motivic Adams-Novikov spectral sequence, and the effective slice spectral sequence. We state some projects for future study.