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arXiv · 2502.13806

Classifying thick subcategories over a Koszul complex via the curved BGG correspondence

Jian Liu·Josh Pollitz
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Abstract

In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is a regular sequence and the classification of thick subcategories for an exterior algebra over a field (via the BGG correspondence). One of the major ingredients is a classification of thick tensor submodules of perfect curved dg modules over a commutative noetherian graded ring concentrated in even degrees, recovering a theorem of Hopkins and Neeman. We give several consequences of the classification result over a Koszul complex, one being that the lattice of thick subcategories of the bounded derived category is fixed by Grothendieck duality.

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BibTeXRIS

Jian Liu, Josh Pollitz. 2025-10-21. Classifying thick subcategories over a Koszul complex via the curved BGG correspondence. https://arxiv.org/abs/2502.13806

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