Koszul and local cohomology, and a question of Dutta

2020/01/31 by Linquan Ma, Anurag K. Singh, Ma, Linquan +3
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2001.11620

openalex publication_date 2020/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a local ring (A,\mathfrakm) of dimension n, we study the natural map from the Koszul cohomology module Hⁿ(\mathfrakm; A) to the local cohomology module Hⁿ_\mathfrakm(A). We prove that the injectivity of this map characterizes the Cohen-Macaulay property of the ring A. We also answer a question of Dutta by constructing normal rings A for which this map is zero.

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