Derived equivalences induced by big cotilting modules

We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module. Moreover, every big cotilting module can be constructed like that in an essentially unique way. We also prove that the triangle equivalence is at the base of an equivalence of derivators, which in turn is induced by a Quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes.Comment: 33 pages; version 2: more details added in Remark 1.11 and in the proofs of Lemmas 1.17 and 4.4, discussion of well-known or inessential results has been reduced (e.g. basics on model structures or the relation to co-t-structures), references have been update

Generating the bounded derived category and perfect ghosts

We show, for a wide class of abelian categories relevant in representation theory and algebraic geometry, that the bounded derived categories have no non-trivial strongly finitely generated thick subcategories containing all perfect complexes. In order to do so we prove a strong converse of the Ghost Lemma for bounded derived categories.Comment: 15 pages; version 2: more details added and presentation improved, reference list expanded and updated including references to examples illustrating our result

On compactly generated torsion pairs and the classification of co-t-structures for commutative noetherian rings

We classify compactly generated co-t-structures on the derived category of a commutative noetherian ring. In order to accomplish that, we develop a theory for compactly generated Hom-orthogonal pairs (also known as torsion pairs in the literature) in triangulated categories that resembles Bousfield localization theory. Finally, we show that the category of perfect complexes over a connected commutative noetherian ring admits only the trivial co-t-structures and (de)suspensions of the canonical co-t-structure and use this to describe all silting objects in the category.Comment: 34 pages. Version 2: minor corrections, references added and update