April 11, 2024Open Access

Length of triangulated categories

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Resumen

We introduce the notion of length of triangulated categories, and we compute the length of the derived category D^ b (C) of a smooth projective curve C and classify all finite length thick subcategories of D^ b (C). We also discuss the length of (1) derived categories of finite dimensional representations of ADE quivers, (2) derived categories of some singular varieties and (3) Krah's phantom subcategories.

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Cite This Study

Hirano et al. (Thu,) studied this question.

synapsesocial.com/papers/68e6f968b6db643587673a3a https://doi.org/https://doi.org/10.48550/arxiv.2404.07583

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3Filtered derived categories of curved deformations2024
4Wide subcategories in extriangulated length categories2026
5Dimension filtration of the bounded Derived category of a Noetherian ring2024

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