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

2018/12/04 by Hu, Po, Kriz, Igor, Somberg, Petr
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1812.01654

Abstract

Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for G=(ℤ/2)ⁿ was completely calculated by Bruner and Greenlees. 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 Bruner and Greenlees, which is in a different form, and hence the comparison involves some non-trivial combinatorics.

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