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Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
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SYSNO ASEP 0541197 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Unbounded derived categories of small and big modules: Is the natural functor fully faithful? Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID
Schnürer, O. M. (DE)Article number 106722 Source Title Journal of Pure and Applied Algebra. - : Elsevier - ISSN 0022-4049
Roč. 225, č. 11 (2021)Number of pages 23 s. Language eng - English Country NL - Netherlands Keywords unbounded derived category ; finitely and infnitely generated modules ; absolute derived category Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA20-13778S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000664028800007 EID SCOPUS 85102506618 DOI 10.1016/j.jpaa.2021.106722 Annotation Consider the obvious functor from the unbounded derived category of all finitely generated modules over a left noetherian ring R to the unbounded derived category of all modules. We answer the natural question whether this functor defines an equivalence onto the full subcategory of complexes with finitely generated cohomology modules in two special cases. If R is a quasi-Frobenius ring of infinite global dimension, then this functor is not full. If R has finite left global dimension, this functor is an equivalence. We also prove variants of the latter assertion for left coherent rings, for noetherian schemes and for locally noetherian Grothendieck categories. 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/10.1016/j.jpaa.2021.106722
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