Rouquier dimension is Krull dimension for normal toric varieties

TL;DR

This paper proves that for normal toric varieties, the Rouquier dimension of their derived category of coherent sheaves equals their Krull dimension, using the coherent-constructible correspondence to relate these concepts.

Contribution

It establishes a precise equality between Rouquier and Krull dimensions for normal toric varieties, a significant link between algebraic and geometric invariants.

Findings

Rouquier dimension equals Krull dimension for all normal toric varieties

The proof employs the coherent-constructible correspondence

Provides a new perspective on derived categories of 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.