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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. Special cases are, 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, the triangulated support and cohomological support of which differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.
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This content will become publicly available on January 10, 2026
Polynomial Functors on Flags
We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite rank groups, and we apply these descriptions to study polynomial representations and representation stability of parabolic subgroups of general linear groups.
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- Award ID(s):
- 1840234
- PAR ID:
- 10610421
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Transformation Groups
- ISSN:
- 1083-4362
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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