Ascent and descent of Artinian module structures under flat base changes

2025/07/25 by Chau, Tran Do Minh, Nhan, Le Thanh
#13D45 #13D45 13B40 #13E05 #13E10 #Commutative Algebra (math.AC) #FOS: Mathematics #N 13B40

paper · doi:10.48550/arxiv.2507.19019

Abstract

Let φ: R→ S be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between R and S are investigated. For an Artinian R-module A, the structure of A⊗_RS is described. As an application, the Artinianess of certain local cohomology modules is clarified.

Citations

• Attached primes of local cohomology modules under localization and completion
• NAK for Ext and Ascent of module structures
• Ascent of module structures, vanishing of Ext, and extended modules
• Top local cohomology and the catenaricity of the unmixed support of a finitely generated module
• Detecting completeness from ext-vanishing

Related

• A note on the non-Artinianness of top local cohomology modules
• Artinianness of local cohomology modules
• Top Local Cohomology Modules Are Almost Always Non-Artinian
• Cosupport of artinian modules
• Ascent of module structures, vanishing of Ext, and extended modules