Establishes that the singularity category of C^*(BG; k) is the bounded derived category of the Ω-Tate spectrum, together with Gorenstein and Tate dualities and a Koszul construction under complete intersection assumptions.
Complete intersections and mod p cochains
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abstract
We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a space, showing that suitable versions of the second and third are equivalent and that the first is stronger. We are particularly interested in classifying spaces of groups, and we give a number of examples. This paper follows on from arXiv:0906.4025 which considered the classical case of a commutative ring and arXiv:0906.3247 which considered the case of rational homotopy theory.
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The singularity category and duality for complete intersection groups
Establishes that the singularity category of C^*(BG; k) is the bounded derived category of the Ω-Tate spectrum, together with Gorenstein and Tate dualities and a Koszul construction under complete intersection assumptions.