The tilting-cotilting correspondence

0537019 - MÚ 2022 RIV US eng J - Journal Article
Positselski, Leonid - Šťovíček, J.
The tilting-cotilting correspondence.
International Mathematics Research Notices. Roč. 2021, č. 1 (2021), s. 191-276. ISSN 1073-7928. E-ISSN 1687-0247
Institutional support: RVO:67985840
Keywords : infinitely generated n-tilting objects * contramoule categories * tilting-cotilting correspondence
OECD category: Pure mathematics
Impact factor: 1.530, year: 2021
Method of publishing: Limited access
https://doi.org/10.1093/imrn/rnz116

To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator and vice versa. Then we construct an equivalence between the (conventional or absolute) derived categories of A and B. Under various assumptions on A⁠, which cover a wide range of examples (for instance, if A is a module category or, more generally, a locally finitely presentable Grothendieck abelian category), we show that B is the abelian category of contramodules over a topological ring and that the derived equivalences are realized by a contramodule-valued variant of the usual derived Hom functor.
Permanent Link: http://hdl.handle.net/11104/0314777