Colocalizing subcategories and cosupport
By D. Benson, S. Iyengar, Henning Krause. 2010
76 citations recorded by the source corpus.
Abstract The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology and cosupport for triangulated categories is developed, building on earlier work of the authors on local cohomology and support.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b74dd3a102e391c9c2ac09e884e6f7f153ccdd2a
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In Algebra and Number Theory
- Greg Stevenson
- S. Iyengar
- Henning Krause
- D. Benson
- J. Pevtsova
- Ryo Takahashi
- Xiao-Wu Chen
- Apostolos Beligiannis
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Stratification for module categories of finite group schemes (2015, methodology): “The cohomology ring H∗(G, k) acts on K(InjG) and, as in [6, 9], the theory of supports and cosupports for StModG extends in a natural way to K(Inj G).”
- Support theory via actions of tensor triangulated categories (2011, methodology): “e of [26] Definition 1.1.4 (we do not assume the strong compatibility conditions between the tensor, internal hom, and triangles, but in order to also define a notion of cosupport for actions following [11] such conditions are likely desirable). In the case that T is rigidly-compactly generated we can”