Tate cohomology of connected k-theory for elementary abelian groups revisited

  • Po Hu
  • Igor KrizEmail author
  • Petr Somberg


Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for \(G=({\mathbb {Z}}/2)^n\) was completely calculated by Bruner and Greenlees (The connective K-theory of finite groups, 2003). In this note, we essentially redo the calculation by a different, more elementary method, and we extend it to \(p>2\) prime. We also identify the resulting spectra, which are products of Eilenberg–Mac Lane spectra, and finitely many finite Postnikov towers. For \(p=2\), we also reconcile our answer completely with the result of [2], which is in a different form, and hence the comparison involves some non-trivial combinatorics.


Tate cohomology Connective K-theory Generalized cohomology 



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© Tbilisi Centre for Mathematical Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA
  3. 3.Faculty of MathematicsMathematical Institute of Charles UniversityPrague 8Czech Republic

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