The singularity category of C^*(BG)

For an ordinary commutative Noetherian ring R we would define the singularity category to be the quotient of the (derived category of) finitely generated modules modulo the (derived category of) fg projective modules [``the bounded derived category modulo compact objects’’]. For a ring spectrum like C^*(BG) (coefficients in a field of characteristic p) it is easy to define the module category and the compact objects, but finitely generated objects need a new definition. The talk will describe the definition and show that the singularity category is trivial exactly when G is p-nilpotent. We will go on to describe the singularity category for groups with cyclic Sylow p-subgroup.