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The tilting-cotilting correspondence
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SYSNO ASEP 0537019 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The tilting-cotilting correspondence Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID
Šťovíček, J. (CZ)Source Title International Mathematics Research Notices. - : Oxford University Press - ISSN 1073-7928
Roč. 2021, č. 1 (2021), s. 191-276Number of pages 86 s. Language eng - English Country US - United States Keywords infinitely generated n-tilting objects ; contramoule categories ; tilting-cotilting correspondence Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000629746000006 EID SCOPUS 85103174026 DOI 10.1093/imrn/rnz116 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022 Electronic address https://doi.org/10.1093/imrn/rnz116
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