• Corpus ID: 235795816

# On realizations of the subalgebra $A^R(1)$ of the $R$-motivic Steenrod Algebra

@inproceedings{Bhattacharya2021OnRO,
title={On realizations of the subalgebra \$A^R(1)\$ of the \$R\$-motivic Steenrod Algebra},
author={Prasit Bhattacharya and Bertrand J. Guillou and Ang Li},
year={2021}
}
• Published 20 June 2021
• Mathematics
. In this paper, we show that the ﬁnite subalgebra A R (1), generated by Sq 1 and Sq 2 , of the R -motivic Steenrod algebra A R can be given 128 diﬀerent A R -module structures. We also show that all of these A -modules can be realized as the cohomology of a 2-local ﬁnite R -motivic spectrum. The realization results are obtained using an R -motivic analogue of the Toda realization theorem. We notice that each realization of A R (1) can be expressed as a coﬁber of an R -motivic v 1 -self-map…

## References

SHOWING 1-10 OF 31 REFERENCES

### The equivariant Thom isomorphism theorem

• Mathematics
• 1992
In this paper we extend ordinary RO(G)-gradeά cohomology to a theory graded on virtual G-bundles over a G-space and show that a Thorn Isomorphism theorem for general (7-vector bundles results. Our

### v1- AND V2-PERIODICITY IN STABLE HOMOTOPY THEORY

• Mathematics
• 1981
this paper we construct some self-maps related to the elements v1 E 7r2(BP) and v2 E 76(BP) and use them to obtain families in the 2-primary stable homotopy of spheres. In particular, we obtain

### EQUIVARIANT ORIENTATIONS AND THOM ISOMORPHISMS

Let G be a compact Lie group and let E∗ G be an RO(G)-graded cohomology theory on G-spaces. We shall explain a sensible way to think about orientations and the Thom isomorphism theorem in the theory

### R-motivic stable stems

• Mathematics
• 2020
We compute some R-motivic stable homotopy groups. For $s - w \leq 11$, we describe the motivic stable homotopy groups $\pi_{s,w}$ of a completion of the R-motivic sphere spectrum. We apply the

### $C_2$-equivariant Homology Operations: Results and Formulas

In this note we state corrected and expanded versions of our previous results on power operations for $C_2$-equivariant Bredon homology with coefficients in the constant Mackey functor on

### 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 Bredon-Landweber region in $C_2$-equivariant stable homotopy groups

• Mathematics
• 2019
We use the $C_2$-equivariant Adams spectral sequence to compute part of the $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{n,n}$. This allows us to recover results of Bredon and Landweber on

### The geometry of iterated loop spaces

Operads and -spaces.- Operads and monads.- A? and E? operads.- The little cubes operads .- Iterated loop spaces and the .- The approximation theorem.- Cofibrations and quasi-fibrations.- The smash