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arXiv · 2509.09941

Regular sequences for triangulated categories

Antonia Kekkou·Janina C. Letz·Marc Stephan
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Abstract

This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local cohomology. The main examples are in the context of the Hochschild cohomology ring or the group cohomology ring acting on derived or stable categories. As applications, lengths of regular sequences provide lower bounds for level and Rouquier dimension.

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Antonia Kekkou, Janina C. Letz, Marc Stephan. 2025-09-12. Regular sequences for triangulated categories. https://arxiv.org/abs/2509.09941

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