English

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}
}

Comments

69 pages