On the cohomology of some Hopf algebroids and Hattori-Stong theorems

Andrew Baker

We apply group cohomological methods to calculate the cohomology of \$\Kn_*\BP\$ as a \$\Kn_*\Kn\$-comodule, recovering recent results of Hovey and Sadofsky. As applications we determine the Chromatic Spectral Sequence for \$\BP\$ based on Johnson and Wilson's \$\En\$, showing the relationship to some generalizations of the classical Hattori-Stong Theorem and determine the change of Hopf algebroid spectral sequence associated with the natural map \$\BP\lra\En\$, extending calculations of Clarke for the Todd orientation \$\MU\lra\KU\$.

Homology, Homotopy and Applications, Vol. 2, 2000, No. 3, pp 29-40

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