A lower bound for the Rouquier dimension of derived categories over commutative rings

Yuki Mifune

A lower bound for the Rouquier dimension of derived categories over commutative rings

Commutative Algebra 2026-06-30 v1 Representation Theory

Authors: Yuki Mifune

Abstract

We prove that the Rouquier dimension of the bounded derived category of finitely generated modules over a commutative noetherian ring is bounded below by the Krull dimension of the ring.

Keywords

Rouquier dimension derived categories commutative rings Krull dimension noetherian rings

Cite

@article{arxiv.2606.31246,
  title  = {A lower bound for the Rouquier dimension of derived categories over commutative rings},
  author = {Yuki Mifune},
  journal= {arXiv preprint arXiv:2606.31246},
  year   = {2026}
}

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5 pages