# 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} }

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

### The second stable homotopy groups of motivic spheres

- 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.

### Stable motivic invariants are eventually étale local

- 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…

### Endomorphisms of the projective plane

- Mathematics
- 2021

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…

### Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map

- Mathematics
- 2021

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…

### On \'etale motivic spectra and Voevodsky's convergence conjecture

- 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

### The first stable homotopy groups of motivic spheres

- MathematicsAnnals 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…

### Motivic Hopf elements and relations

- 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…

### Low-dimensional Milnor–Witt stems over ℝ

- 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…

### The second stable homotopy groups of motivic spheres

- 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.

### Reduced power operations in motivic cohomology

- Mathematics
- 2001

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…

### A comparison of motivic and classical stable homotopy theories

- Mathematics
- 2011

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.…

### On very effective hermitian K-theory

- MathematicsMathematische 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…

### Rigidity in motivic homotopy 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.

### Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms

- 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…

### On the Motivic π0 of the Sphere Spectrum

- Mathematics
- 2004

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…