Rouquier dimension is Krull dimension for normal toric varieties

David Favero; Jesse Huang

doi:10.1007/s40879-023-00686-1

Rouquier dimension is Krull dimension for normal toric varieties

David Favero, Jesse Huang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Article number	91
Journal	European Journal of Mathematics
Volume	9
Issue number	4
DOIs	https://doi.org/10.1007/s40879-023-00686-1
State	Published - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Derived categories
Rouquier dimension
Toric varieties

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10.1007/s40879-023-00686-1

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title = "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.",

keywords = "Derived categories, Rouquier dimension, Toric varieties",

author = "David Favero and Jesse Huang",

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doi = "10.1007/s40879-023-00686-1",

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AU - Favero, David

AU - Huang, Jesse

PY - 2023/12

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AB - 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.

KW - Derived categories

KW - Rouquier dimension

KW - Toric varieties

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Rouquier dimension is Krull dimension for normal toric varieties

Abstract

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