Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rouquier dimension is Krull dimension for normal toric varieties

David Favero, Jesse Huang

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.

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.
Paper Structure (3 sections, 15 theorems, 51 equations)

This paper contains 3 sections, 15 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Generation time for probe generators
  3. Application to toric varieties

Key Result

Theorem 1.2

For any normal toric variety Conjecture conj: Orlov holds.

Theorems & Definitions (38)

  • Conjecture 1.1: Orlov
  • Theorem 1.2: =Corollary \ref{['cor: rdim=dim variety']}
  • Theorem 1.3: =Example \ref{['ex: torus']}
  • Lemma 2.1
  • proof
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Proposition 2.5
  • proof
  • ...and 28 more