Generating the bounded derived category and perfect ghosts (Q2880380)

In the main result of the paper (Theorem 2) it is proved that if \(\mathcal{T}\) is a big enough strongly finitely generated thick subcategory of the bounded derived category associated to \(\text{mod-}\Lambda\) (where \(\Lambda\) is a noetherian algebra) or to \(\text{coh}\mathbb{X}\) (\(\mathbb{X}\) is a projective scheme over a commutative noetherian ring) then \(\mathcal{T}\) is in fact the whole bounded derived category. There are two very interesting ingredients for the proof of this result: (1) for the above mentioned derived categories the converse of the ghost lemma is valid (see Theorem 2); (2) in some natural hypotheses an object \(Y\in \mathbf{D}^{-}(\mathcal{A})\) (where \(\mathcal{A}\) is a skeletally small abelian category) is cocompact if and only if it is isomorphic to a bounded complex (Theorem 18).