# Remarks on motivic Moore spectra

@article{Rondigs2019RemarksOM,
title={Remarks on motivic Moore spectra},
author={Oliver Rondigs},
journal={Motivic Homotopy Theory and Refined
Enumerative Geometry},
year={2019}
}
• O. Rondigs
• Published 2 October 2019
• Mathematics
• Motivic Homotopy Theory and Refined Enumerative Geometry
The term “motivic Moore spectrum” refers to a cone of an element α : Σ1 → 1 in the motivic stable homotopy groups of spheres. Homotopy groups, multiplicative structures, and Voevodsky’s slice spectral sequence are discussed for motivic Moore spectra.
5 Citations
• Mathematics
• 2021
We compute the 2-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of motivic cohomology and hermitian K-groups.
• Mathematics
• 2020
In this paper we prove a Thomason-style descent theorem for the $\rho$-complete sphere spectrum. In particular, we deduce a very general etale descent result for torsion, $\rho$-complete motivic
The endomorphism ring of the projective plane over a field F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy category than in
The endomorphism ring of the projective plane over a ﬁeld F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy category than in
• Mathematics
• 2020
We prove a new convergence result for the slice spectral sequence, following work by Levine and Voevodsky. This verifies a derived variant of Voevodsky’s conjecture on convergence of the slice

## References

SHOWING 1-10 OF 24 REFERENCES

• Mathematics
Annals of Mathematics
• 2019
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
• Mathematics
• 2013
We use Cayley-Dickson algebras to produce Hopf elements eta, nu and sigma in the motivic stable homotopy groups of spheres, and we prove via geometric arguments that the the products eta*nu and
• Mathematics
• 2017
This article computes some motivic stable homotopy groups over R. For 0 <= p - q <= 3, we describe the motivic stable homotopy groups of a completion of the motivic sphere spectrum. These are the
• Mathematics
• 2021
We compute the 2-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of motivic cohomology and hermitian K-groups.
In this paper we construct an analog of Steenrod operations in motivic cohomology and prove their basic properties including the Cartan formula, the Adem relations and the realtions to characteristic
Let k be an algebraically closed field of characteristic zero. Let c:𝒮ℋ→𝒮ℋ(k) be the functor induced by sending a space to the constant presheaf of spaces on Sm/k. We show that c is fully faithful.
• Mathematics
Mathematische Zeitschrift
• 2019
We argue that the very effective cover of hermitian K-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topological K-theory
• Mathematics
• 2008
We show that extensions of algebraically closed fields induce full and faithful functors between the respective motivic stable homotopy categories with finite coefficients.
• Mathematics
• 2016
We advance the understanding of K-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K-groups and Witt-groups. By an explicit computation of the slice
Let d ≥ 1 and X a pointed topological space. We denote as usual by π d (X) the d-th homotopy group of X. One of the starting point in homotopy theory is the following result: Theorem 1.1.1. Let n > 0