Tensor triangular geometry and KK-theory

Abstract

We present some results on equivariant KK-theory in the context of tensor triangular geometry. More specifically, for G a finite group, we show that the spectrum of the tensor triangulated subcategory of KK^G generated by the tensor unit contains as a retract a canonical copy of the Zariski spectrum of the complex character ring of G. For G trivial, this inclusion is a homeomorphism. We also prove a general criterion for a support theory on a compactly generated tensor triangulated category to provide the universal support datum, in the sense of Paul Balmer, on its subcategory of compact objects.

33 pages, updated some references as in published version

References in corpus (1)

• Homological algebra in bivariant K-theory and other triangulated categories

Cited by in corpus (7)

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