Geodesic
On connective $K$-theory of elementary abelian $2$-groups and local duality
Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 215-243.

Voir la notice de l'article provenant de la source International Press of Boston

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 $Q_0, Q_1$ 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.
DOI : 10.4310/HHA.2014.v16.n1.a13
Classification : 19L41, 20J06
Keywords: connective $K$-theory, elementary abelian group, group cohomology, group homology, local cohomology 
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Geoffrey M. L. Powell. On connective $K$-theory of elementary abelian $2$-groups and local duality. Homology, homotopy, and applications, Tome 16 (2014) no. 1, pp. 215-243. doi : 10.4310/HHA.2014.v16.n1.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2014.v16.n1.a13/

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