On the 𝐵𝑃⟨𝑛⟩-cohomology of elementary abelian 𝑝-groups

Powell, Geoffrey

doi:10.1090/tran6699

On the $BP\langle n\rangle$-cohomology of elementary abelian $p$-groups
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Trans. Amer. Math. Soc. 368 (2016), 8029-8046 Request permission

Abstract:

The structure of the $BP\langle n\rangle$-cohomology of elementary abelian $p$-groups is studied, obtaining a presentation expressed in terms of $BP$- cohomology and mod-$p$ singular cohomology, using the Milnor derivations.

The arguments are based on a result on multi-Koszul complexes which is related to Margolis’s criterion for freeness of a graded module over an exterior algebra.

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