Hartshorne's questions and weakly cofiniteness

2018/01/23 by Hajar Roshan-Shekalgourabi, Roshan-Shekalgourabi, Hajar, Hatamkhani, Marzieh
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1801.07768

Abstract

Let R be a commutative Noetherian ring, \fa be an ideal of R and M be an R-module. The main purpose of this paper is to answer the Hartshorn's questions in the class of weakly Laskerian modules. It is shown that if s≥ 1 is a positive integer such that \Ext^j_R(R/\fa, M) is weakly Laskerian for all j≤ s and the R-module Hⁱ_\fa(M) is FD_{≤ 1} for all i < s, then the R-module Hⁱ_\fa(M) is \fa-weakly cofinite for all i

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