Weakly approximable triangulated categories and enhancements: a survey

Alberto Canonaco; Amnon Neeman; Paolo Stellari

Weakly approximable triangulated categories and enhancements: a survey

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arxiv 2407.05946 v2 pith:NMJ7LSKP submitted 2024-07-08 math.AG math.CTmath.RT

Alberto Canonaco , Amnon Neeman , Paolo Stellari This is my paper · ORCID

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This paper surveys some recent results, concerning the intrinsicness of natural subcategories of weakly approximable triangulated categories. We also review the results about uniqueness of enhancements of triangulated categories, with the aim of showing the fruitful interplay. In particular, we show how this leads to a vast generalization of a result by Rickard about derived invariance for schemes and rings.

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Approximable Triangulated Categories and Reflexive DG-categories
math.AG 2024-11 accept novelty 6.0 of 10

A locally finite approximable DG-category with a strong generator inside its finitely valued modules is finite-reflexive; this yields reflexivity for proper schemes, Azumaya algebras, and proper connective DG-algebras.

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