0541197 - MÚ 2022 RIV NL eng J - Journal Article
Positselski, Leonid - Schnürer, O. M.
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
Journal of Pure and Applied Algebra. Roč. 225, č. 11 (2021), č. článku 106722. ISSN 0022-4049. E-ISSN 1873-1376
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : unbounded derived category * finitely and infnitely generated modules * absolute derived category
OECD category: Pure mathematics
Impact factor: 0.834, year: 2021 ; AIS: 0.785, rok: 2021
Method of publishing: Limited access
Result website:
https://doi.org/10.1016/j.jpaa.2021.106722DOI: https://doi.org/10.1016/j.jpaa.2021.106722

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.
Permanent Link: http://hdl.handle.net/11104/0318796