The Rouquier dimension of the category of perfect complexes over a regular ring

TL;DR

This paper proves that the Rouquier dimension of perfect complexes over a regular ring equals the ring's Krull dimension, establishing a precise measure that was previously only bounded above.

Contribution

It establishes the exact Rouquier dimension for perfect complexes over regular rings, linking it to Krull dimension and regular sequence length, including new results for regular local rings.

Findings

Rouquier dimension equals Krull dimension for regular rings

Lower bound given by maximal length of regular sequence

New result for regular local rings

Abstract

We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not known in general. In particular, for regular local rings this result is new. More generally, we show that a lower bound of the Rouquier dimension is given by the maximal length of a regular sequence.