The derived category analogue of the Hartshorne-Lichtenbaum Vanishing Theorem

2012/08/22 by Hatamkhani, Marziyeh, Divaani-Aazar, Kamran
#13D02 #13D45 #14B15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1208.4447

Abstract

Let \fa be an ideal of a local ring (R,\fm) and X a d-dimensional homologically bounded complex of R-modules whose all homology modules are finitely generated. We show that H^d_\fa(X)=0 if and only if dim R/\fa R+\fp>0 for all prime ideals \fp of R such that dim R/\fp-inf (X⊗_RR)_\fp=d.

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