Derived category of permutation modules and cohomological singularity
We consider the bounded derived category of finitely generated representations of a finite group, with coefficients in a noetherian commutative ring. We construct an invariant that detects which part of this derived category is controlled by permutation modules. This invariant uses group cohomology and takes values in the singularity category of the coefficient ring. We then discuss variants for big triangulated categories and propose a definition of the big derived category of permutation modules.