In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a commutative noetherian ring
Let
 NSFPAR ID:
 10506375
 Editor(s):
 Dan Abramovich
 Publisher / Repository:
 Amer. Math. Soc.
 Date Published:
 Journal Name:
 Transactions of the American Mathematical Society
 ISSN:
 00029947
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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$R$ and complexes of$R$ modules with finitely generated homology$M$ and$N$ , we show$N$ is in the thick subcategory generated by$M$ if and only if the ghost index of$N_\mathfrak {p}$ with respect to$M_\mathfrak {p}$ is finite for each prime$\mathfrak {p}$ of$R$ . To do so, we establish a “converse coghost lemma” for the bounded derived category of a nonnegatively graded DG algebra with noetherian homology. 
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