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arXiv · 2605.13416

Remarks on diagonal dimension for algebraic stacks

Pat Lank·Fei Peng
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Abstract

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 classical generators of a fibre product, recovering a result of Elagin--Lunts--Schn\"{u}rer. Finally, we show that the diagonal dimension of a variety in arbitrary characteristic with mild singularities is at most twice its Krull dimension.

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Pat Lank, Fei Peng. 2026-05-13. Remarks on diagonal dimension for algebraic stacks. https://arxiv.org/abs/2605.13416

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