A partial converse ghost lemma for the derived category of a commutative Noetherian ring

In this article a condition is given to detect the containment among thick subcategories of bounded derived category commutative noetherian ring. More precisely, for ring R R and complexes -modules with finitely generated homology M"> M encoding="application/x-tex">M N"> N encoding="application/x-tex">N , we show in subcategory by if only ghost index N Subscript German p"> p encoding="application/x-tex">N_\mathfrak {p} respect M encoding="application/x-tex">M_\mathfrak finite each prime alttext="German encoding="application/x-tex">\mathfrak . To do so, establish “converse coghost lemma” non-negatively graded DG algebra homology.