Classifying thick subcategories over a Koszul complex via the curved BGG correspondence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917029731106816 |
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| author | Liu, Jian Pollitz, Josh |
| author_facet | Liu, Jian Pollitz, Josh |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classifying thick subcategories over a Koszul complex via the curved BGG correspondence Liu, Jian Pollitz, Josh Commutative Algebra Representation Theory 13D09 (primary), 14M10, 18G80 (secondary) 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. |
| title | Classifying thick subcategories over a Koszul complex via the curved BGG correspondence |
| topic | Commutative Algebra Representation Theory 13D09 (primary), 14M10, 18G80 (secondary) |
| url | https://arxiv.org/abs/2502.13806 |