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Article Dans Une Revue Homology, Homotopy and Applications Année : 2014

On connective K-theory of elementary abelian 2-groups and local duality

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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.

Dates et versions

hal-03038378 , version 1 (03-12-2020)

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Geoffrey Powell. On connective K-theory of elementary abelian 2-groups and local duality. Homology, Homotopy and Applications, 2014, 16 (1), pp.215-243. ⟨10.4310/HHA.2014.v16.n1.a13⟩. ⟨hal-03038378⟩
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