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# Homology, Homotopy and Applications

## Volume 11 (2009)

### Number 2

### The cohomology of motivic $A(2)$

Pages: 251 – 274

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n2.a13

#### Author

#### Abstract

Working over an algebraically closed field of characteristic zero, we compute the cohomology of the subalgebra $A(2)$ of the motivic Steenrod algebra that is generated by $Sq^1$, $Sq^2$, and $Sq^4$. The method of calculation is a motivic version of the May spectral sequence.

Speculatively assuming that there is a “motivic modular forms” spectrum with certain properties, we use an Adams-Novikov spectral sequence to compute the homotopy of such a spectrum at the prime 2.

#### Keywords

May spectral sequence, motivic homotopy theory, motivic cohomology, Steenrod algebra

#### 2010 Mathematics Subject Classification

14F42, 55S10, 55T15

Published 1 January 2009