2016/12/01 by Douglas J. Dailey, Srikanth B. Iyengar, Dailey, Douglas J. +3
Mathematics · #13D05 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1612.00509
openalex publication_date 2016/12/01 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
It is proved that a module M over a Noetherian ring R of positive\ncharacteristic p has finite flat dimension if there exists an integer t\≥\n0 such that \ToriR(M, ^fe !R)=0 for t\≤ i\≤ t+\dim\nR and infinitely many e. This extends a result of Herzog, who proved it when\nM is finitely generated, and strengthens a result of the third author and\nWebb in the case M is arbitrary. It is also proved that when R is a\nCohen-Macaulay local ring, it suffices that the Tor vanishing holds for one\ne\≥ \logpe(R), where e(R) is the multiplicity of R.\n