Support theory via actions of tensor triangulated categories

Details Support theory via actions of tensor triangulated categories Support theory via actions of tensor triangulated categories

2011-05-24

arxiv.org/abs/1105.4692v2

Mathematics

Category Theory

33 pages, comments welcome; reformatted and made minor corrections

Scientific paper

We give a definition of the action of a tensor triangulated category T on a triangulated category K. In the case that T is rigidly-compactly generated and K is compactly generated we show this gives rise to a notion of supports which categorifies work of Benson, Iyengar, and Krause and extends work of Balmer and Favi. We prove that a suitable version of the local-to-global principle holds very generally. A relative version of the telescope conjecture is formulated and we give a sufficient condition for it to hold.

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