2025/08/07 by Sadeqi, Behruz
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.05051
This article investigates the relationship between Betti numbers of finitely generated modules over a Noetherian local ring (R, \mathfrakm) and the structure of formal local cohomology modules. We establish a connection between the vanishing of formal local cohomology and the depth of a module, generalizing classical results. The main theorem links the Betti numbers to the Artinian property of formal local cohomology modules, and we provide applications to Cohen-Macaulay rings. Original proofs are given for all stated results.