Local cohomology and support for triangulated categories
Dave Benson, Srikanth B. Iyengar, Henning Krause
Abstract
We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Suitably specialized one recovers, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects whose triangulated support and cohomological support differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.
Create a lesson
Related papers
Gerstenhaber algebra structure on the Hochschild cohomology ring of the Xu--Snashall algebra
Qi Long, Ziyang Shi, Guodong Zhou
K-theory of Matroids and Monoid Schemes
Christian Haesemeyer, Charles A. Weibel
On motivic cohomology of commutative C*-algebras
Ko Aoki
The Nil K-groups of finite groups
Ted Chinburg, Matthew Morrow, Georgios Pappas et al.
The Oka principle for étale Chow groups
Ko Aoki
General linear and Steinberg groups over the Leavitt algebra L F2(1,2)
Huynh Viet Khanh