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

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

http://www.rmi.acnet.ge/hha/volumes/2000/n3/n3.dvi (ps, dvi.gz, ps.gz)

ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2000/n3/n3.dvi (ps, dvi.gz, ps.gz)