The singularity category and duality for complete intersection groups
Abstract
Abstract If is a finite group, the structure of the modular representation theory depends on the cochains , viewed as a commutative ring spectrum. We consider here its singularity category (in the sense of the author and Stevenson [Adv. Math. 365 (2020), 44 pp., arXiv:1702.07957]) and show that the singularity category is the bounded derived category of the ‐Tate spectrum (the ‐nullification of the Koszul dual connective ring spectrum ). We establish a form of Gorenstein duality for , and show that the ‐Tate spectrum enjoys a form of Tate duality. Under a complete intersection hypothesis we give a method for calculating the ‐Tate homology.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 6
- Publication date
- 1 June 2026
- Language
- EN