On connective K-theory of elementary abelian 2-groups and local duality
Résumé
The connective ku-(co)homology of elementary abelian 2-groups is determined as a functor of the elementary abelian 2-group, using the action of the Milnor operations Q0,Q1 on mod 2 group cohomology, the Atiyah-Segal theorem for KU-cohomology, together with an analysis of the functorial structure of the integral group ring; the functorial structure then reduces calculations to the rank 1 case.
These results are used to analyse the local cohomology spectral sequence calculating ku-homology, via a functorial version of local duality for Koszul complexes, giving a conceptual explanation of results of Bruner and Greenlees.