Tensor triangular geometry and KK-theory

Details Tensor triangular geometry and KK-theory Tensor triangular geometry and KK-theory

2010-01-15

arxiv.org/abs/1001.2637v2

J. Homotopy Relat. Struct., vol. 5(1), 2010, pp.319-358

Mathematics

K-Theory and Homology

33 pages, updated some references as in published version

Scientific paper

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.

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