Homology, Homotopy and Applications

Volume 11 (2009)

Number 2

The cohomology of motivic $A(2)$

Pages: 251 – 274

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

Author

Daniel C. Isaksen (Department of Mathematics, Wayne State University, Detroit, Michigan, U.S.A.)

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

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