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Three notions of dimension for triangulated categories

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arxiv 1901.09461 v2 pith:5PMKCCTA submitted 2019-01-27 math.AG math.CT

Alexey Elagin , Valery A. Lunts This is my paper · ORCID
classification math.AGmath.CT
keywords dimensioncategoriesdiscussnotionsthreetriangulatedbasiccompare
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In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.

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  1. Rouquier dimension of some blow-ups

    math.AG 2019-08 conditional novelty 7.0 of 10

    Certain blow-ups of projective spaces, including the plane in up to nine points, satisfy Orlov's conjecture that the Rouquier dimension of the derived category equals the dimension.

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