Coartinianess of extension and torsion functors

2022/06/10 by Jingwen Shen, Shen, Jingwen, Yang Xiaoyan +1
Mathematics · #13C15 #13H10 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2206.04961

openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (R,\mathfrakm) be a commutative noetherian local ring with \mathfrakm-adic topology, I an ideal of R. We investigate coartinianess of Ext and Tor, show that the R-module Ext_Rⁱ(N,M) is I-coartinian if M is a linearly compact I-coartinian R-module and N is an I-cofinite R-module of dimension at most 1; the R-module Tor_i^R(N,M) is I-coartinian in the case M is semi-discrete linearly compact I-coartinian and N is finitely generated with dimension at most 2.

Related

• Coartinianess of local homology modules for ideals of small dimension
• Extension functors of local cohomology modules
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