Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
| Autor: | Olaf M. Schnürer, Leonid Positselski |
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| Rok vydání: | 2020 |
| Předmět: |
Noetherian
Pure mathematics Primary 18G80 Secondary 16E35 16L60 18G20 18E10 01 natural sciences Global dimension Mathematics - Algebraic Geometry Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Category Theory (math.CT) 0101 mathematics Representation Theory (math.RT) Algebraic Geometry (math.AG) Mathematics Subcategory Ring (mathematics) Derived category Noetherian ring Algebra and Number Theory Functor Mathematics::Commutative Algebra 010102 general mathematics Mathematics - Category Theory K-Theory and Homology (math.KT) Mathematics - Rings and Algebras Cohomology Rings and Algebras (math.RA) Mathematics - K-Theory and Homology 010307 mathematical physics Mathematics - Representation Theory |
| DOI: | 10.48550/arxiv.2003.11261 |
| Popis: | 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. Comment: 23 pages, typo corrected |
| Databáze: | OpenAIRE |
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