Cohomologically Cofinite Complexes

2012/08/20 by Porta, Marco, Shaul, Liran, Yekutieli, Amnon · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1208.4064

Abstract

Let A be a commutative noetherian ring, and \a an ideal in it. In this paper we continue the study, begun in [PSY1], of the derived \a-adic completion and the derived \a-torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.

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• Torsion and complete dualizable objects in tensor-triangulated categories over a Noetherian ring

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