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arXiv · 2411.09461

Approximable Triangulated Categories and Reflexive DG-categories

Isambard Goodbody·Theo Raedschelders·Greg Stevenson
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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.

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Isambard Goodbody, Theo Raedschelders, Greg Stevenson. 2024-11-14. Approximable Triangulated Categories and Reflexive DG-categories. https://arxiv.org/abs/2411.09461

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