Asymptotic behavior of Ext for pairs of modules of large complexity over graded complete intersections

2020/12/19 by David A. Jorgensen, Jorgensen, David A., Liana M. Şega +3 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2012.10670

openalex publication_date 2020/12/19 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28

Abstract

Let M and N be finitely generated graded modules over a graded complete intersection R such that Ext_Rⁱ(M,N) has finite length for all i≫ 0. We show that the even and odd Hilbert polynomials, which give the lengths of Extⁱ_R(M,N) for all large even i and all large odd i, have the same degree and leading coefficient whenever the highest degree of these polynomials is at least the dimension of M or N. Refinements of this result are given when R is regular in small codimensions.

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• Multiplicity in triangulated categories

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