Approximable Triangulated Categories and Reflexive DG-categories
Algebraic Geometry
2025-05-16 v3 Representation Theory
Abstract
We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable triangulated category under a properness assumption. We apply our results to proper schemes, proper connective DG-algebras and Azumaya algebras over proper schemes. We include an appendix by Raedschelders and Stevenson showing that proper connective DG-algebras admit finite dimensional models over any field.
Cite
@article{arxiv.2411.09461,
title = {Approximable Triangulated Categories and Reflexive DG-categories},
author = {Isambard Goodbody and Theo Raedschelders and Greg Stevenson},
journal= {arXiv preprint arXiv:2411.09461},
year = {2025}
}
Comments
- Appendix added by Raedschelders and Stevenson - Minor fixes