Unbounded derived categories of small and big modules: Is the natural functor fully faithful?

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541197" target="_blank" >RIV/67985840:_____/21:00541197 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2021.106722" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106722</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106722" target="_blank" >10.1016/j.jpaa.2021.106722</a>

Result language
angličtina
Original language name
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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