Derived functors and Hilbert polynomials over hypersurface rings

2024/04/23 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13A30 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Holomorphic and Operator Theory #Primary 13D09 #Secondary 13H10

paper · pdf · doi:10.48550/arxiv.2404.14938

openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (A,\mathfrakm) be a hypersurface local ring of dimension d ≥ 1 and let I be an \mathfrakm-primary ideal. We show that there is a non-negative integer r_I (depending only on I) such that if M is any non-free maximal Cohen-Macaulay A-module the function n → ℓ(Tor^A₁(M, A/Iⁿ⁺¹)) (which is of polynomial type) has degree r_I. 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).

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