Derived equivalences induced by big cotilting modules

By J. Št’ovíček. 2013

63 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9020afbbdfb3e4f84623bc41e867cf7813db68a5

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

∞-tilting theory (2017, methodology): “A correspondence between n-cotilting modules and small n-tilting objects in Grothendieck abelian categories together with the related derived equivalence were constructed by the second author of the present paper [52].”
The Tilting–Cotilting Correspondence (2017, background): “Based on an existing theory of infinitely generated (co)tilting modules, similar results were obtained in [81] in the case”
Silting Objects (2018, methodology): “Over the years, this result has successively been extended to more general situations [52, 94, 90, 50, 84, 88, 45, 97], leading to a derived Morita theory for Grothendieck categories.”
Realisation functors in tilting theory (2015, methodology): “In representation theory, there are some motivating predecessors of the non-compact tilting theory that we develop in this paper: large tilting and cotilting modules over rings ([4,29,30,77]) and large silting”