Remarks on motivic Moore spectra

TL;DR

This paper explores properties of motivic Moore spectra, focusing on their ring structures and the role of Toda brackets within the motivic stable homotopy groups of spheres.

Contribution

It investigates whether the ring structure of the motivic sphere spectrum extends to motivic Moore spectra, providing insights into their algebraic properties.

Findings

Analysis of Toda brackets in motivic stable homotopy groups

Discussion on the descent of ring structures to motivic Moore spectra

Insights into the algebraic and homotopical properties of motivic Moore spectra

Abstract

The term "motivic Moore spectrum" refers to a cone of an element in the motivic stable homotopy groups of spheres. This article discusses some properties of motivic Moore spectra, among them the question whether the ring structure on the motivic sphere spectrum descends to a ring structure on a motivic Moore spectrum. This discussion requires an understanding of some Toda brackets in the motivic stable homotopy groups of spheres.