On the BP<n>-cohomology of elementary abelian p-groups

TL;DR

This paper investigates the structure of BP<n>-cohomology for elementary abelian p-groups, providing a presentation that combines BP-cohomology and mod-p cohomology using Milnor derivations.

Contribution

It introduces a new presentation of BP<n>-cohomology for elementary abelian p-groups leveraging Milnor derivations and multi-Koszul complexes.

Findings

Derived a presentation of BP<n>-cohomology in terms of known cohomologies.

Connected multi-Koszul complexes with Margolis's criterion for module freeness.

Enhanced understanding of the algebraic structure of BP<n>-cohomology.

Abstract

The structure of the BP<n>-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.