Support theory via actions of tensor triangulated categories
By Greg Stevenson. 2011
83 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/1b7ccdbae78424951cebd2cca22fecdfcfc358af
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Subcategories of singularity categories via tensor actions (2011, methodology): “As in [43] this gives rise to a theory of supports for objects of S(X), and hence DSg(X), taking values in X .”