Remarks on diagonal dimension for algebraic stacks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918499628089344 |
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| author | Lank, Pat Peng, Fei |
| author_facet | Lank, Pat Peng, Fei |
| contents | This note is concerned with the Rouquier dimension of the bounded derived category of coherent complexes on a Noetherian algebraic stack. Specifically, we study the diagonal dimension of a morphism, which can be used to produce upper bounds on Rouquier dimension. First, we obtain an explicit upper bound for smooth morphisms with a regular target. Second, we identify strong generators of a fiber product, recovering a result of Elagin--Lunts--Schnürer. Finally, we show that the diagonal dimension of a variety in arbitrary characteristic with mild singularities is at most twice its Krull dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13416 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remarks on diagonal dimension for algebraic stacks Lank, Pat Peng, Fei Algebraic Geometry Commutative Algebra 14A30 (primary), 14A20, 13A35 This note is concerned with the Rouquier dimension of the bounded derived category of coherent complexes on a Noetherian algebraic stack. Specifically, we study the diagonal dimension of a morphism, which can be used to produce upper bounds on Rouquier dimension. First, we obtain an explicit upper bound for smooth morphisms with a regular target. Second, we identify strong generators of a fiber product, recovering a result of Elagin--Lunts--Schnürer. Finally, we show that the diagonal dimension of a variety in arbitrary characteristic with mild singularities is at most twice its Krull dimension. |
| title | Remarks on diagonal dimension for algebraic stacks |
| topic | Algebraic Geometry Commutative Algebra 14A30 (primary), 14A20, 13A35 |
| url | https://arxiv.org/abs/2605.13416 |