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A localisation theorem for singularity categories of proper dg algebras

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arxiv 2302.05054 v2 pith:5Y7Q7EOB submitted 2023-02-10 math.RT

Haibo Jin , Dong Yang , Guodong Zhou This is my paper · ORCID
classification math.RT
keywords algebrascategoriessingularityproperringthreeallowsbase
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Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of their singularity categories. This allows us to recover and generalise some known results on singularity categories of finite-dimensional algebras.

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  1. Extension dimensions under singular equivalences and recollements

    math.RT 2025-02 conditional novelty 7.0 of 10

    Artin algebras connected by recollements or singular equivalences of Morita type with level l satisfy explicit inequalities on their extension dimensions, with Omega-extension dimension invariant in the singular case.

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