Rouquier dimension is Krull dimension for normal toric varieties

Abstract

We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull dimension. Our proof uses the coherent-constructible correspondence to translate the problem into the study of Rouquier dimension for certain categories of constructible sheaves.

arXiv comment9 pages. Added acknowledgements and additional citations. Small errors and typos fixed

References in corpus (5)

• Orlov spectra: bounds and gaps
• The nonequivariant coherent-constructible correspondence for toric stacks
• A categorification of Morelli's theorem
• Toric Stacks I: The Theory of Stacky Fans
• The toric Frobenius morphism and a conjecture of Orlov

Cited by in corpus (4)

• Resolutions of toric subvarieties by line bundles and applications
• A short proof of the Hanlon-Hicks-Lazarev Theorem
• High Frobenius pushforwards generate the bounded derived category
• Explicit constructions of short virtual resolutions of truncations