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Specialization finite group schemes with applications to ( co )-stratification and local duality

Let R be a commutative Noetherian ring, and consider the derived category of ModR, T = D(R). The compact objects of T form the bounded derived category of perfect complex over R, T c = D(R). For a complex M in D(R), and a prime p ∈ SpecR, we can consider the localization Mp of M at p and the specialization M⊗Rk(p) at p, invariants which provide “local information” about the complex M at the point p. One invariant we can use this local information for is the support.