Derived functors and Hilbert polynomials over hypersurface rings

Let (A,m) be a hypersurface local ring of dimension d ≥ 1 and let I be an m-primary ideal. We show that there is a non-negative integer rI (depending only on I) such that if M is any non-free maximal Cohen-Macaulay A-module the function n → (TorA₁(M, A/Iⁿ⁺¹)) (which is of polynomial type) has degree rI. Analogous results hold for Hilbert polynomials associated to Ext-functors. Surprisingly a key ingredient is the classification of thick subcategories of the stable category of MCM A-modules (obtained by Takahashi).