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.
Uniqueness of enhancements for derived and geometric categories / A. Canonaco, A. Neeman, P. Stellari. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 10:(2022), pp. e92.1-e92.65. [10.1017/fms.2022.82]
Uniqueness of enhancements for derived and geometric categories
P. Stellari
Ultimo
2022
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.File | Dimensione | Formato | |
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