Related papers: R-motivic stable stems

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 first four Milnor-Witt stems. We start with…

We present a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. We use the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C…

We study the stable motivic homotopy groups $\pi_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an…

We use an Adams spectral sequence to calculate the R-motivic stable homotopy groups after inverting eta. The first step is to apply a Bockstein spectral sequence in order to obtain h_1-inverted R-motivic Ext groups, which serve as the input…

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…

We establish an isomorphism between the stable homotopy groups of the 2-completed motivic sphere spectrum over the real numbers and the corresponding stable homotopy groups of the 2-completed Z/2-equivariant sphere spectrum, in a certain…

These notes, written version of a Bourbaki talk, survey Morel-Voevodsky's motivic homotopy theory over a field, with a focus on computations of motivic homotopy sheaves, both stable and unstable. We also describe Isaksen-Wang-Xu's…

A C-motivic modular forms spectrum mmf has recently been constructed. This article presents detailed computational information on the Adams spectral sequence for mmf. This information is essential for computing with the C-motivic and…

We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…

We compute the $v_1$-periodic $\mathbb{R}$-motivic stable homotopy groups. The main tool is the effective slice spectral sequence. Along the way, we also analyze $\mathbb{C}$-motivic and $\eta$-periodic $v_1$-periodic homotopy from the same…

We compute the h_1-localized cohomology of the motivic Steenrod algebra over C. This serves as the input to an Adams spectral sequence that computes the motivic stable homotopy groups of the eta-local motivic sphere. We compute some of the…

In this paper we explore the isotropic stable motivic homotopy category constructed from the usual stable motivic homotopy category, following the work of Vishik on isotropic motives (see [29]), by killing anisotropic varieties. In…

We compute the cohomology of the quotient algebra $\mathcal{A}(2)$ of the $\mathbb{R}$-motivic dual Steenrod algebra. We do so by running a $\rho$-Bockstein spectral sequence whose input is the cohomology of $\mathbb{C}$-motivic…

We study the $\mathbb{F}_2$-synthetic Adams spectral sequence. We obtain new computational information about $\mathbb{C}$-motivic and classical stable homotopy groups.

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.

This document contains large-format Adams charts that compute 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. The charts are essentially complete through the 61-stem and contain partial…

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…

We establish a differential $d_2(D_1)=h_0^2h_3g_2$ in the $51$-stem of the Adams spectral sequence at the prime $2$, which gives the first correct calculation of the stable 51 and 52 stems. This differential is remarkable since we know of…

Let k be a field with cohomological dimension less than 3; we call such fields low-dimensional. Examples include algebraically closed fields, finite fields and function fields thereof, local fields, and number fields with no real…

We compute the 2-primary $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{s,c}$ for stems between 0 and 25 (i.e., $0 \leq s \leq 25$) and for coweights between -1 and 7 (i.e., $-1 \leq c \leq 7)$. Our results, combined with periodicity…