Uniqueness of enhancements for derived and geometric categories
Algebraic Geometry
2021-01-13 v1 Category Theory
K-Theory and Homology
Abstract
We prove that the derived categories of abelian categories have unique enhancements -- all of them, the unbounded, bounded, bounded above and bounded below derived categories. The unseparated and left completed derived categories of a Grothendieck abelian category are also shown to have unique enhancements. Finally we show that the derived category of complexes with quasi-coherent cohomology and the category of perfect complexes have unique enhancements for quasi-compact and quasi-separated schemes.
Keywords
Cite
@article{arxiv.2101.04404,
title = {Uniqueness of enhancements for derived and geometric categories},
author = {Alberto Canonaco and Amnon Neeman and Paolo Stellari},
journal= {arXiv preprint arXiv:2101.04404},
year = {2021}
}
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69 pages