Article
| Title: | Filtrations by cosupports via tensor actions (English) |
| Author: | Xu, Peng |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 1017-1027 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Suppose $\mathcal {T}$ is a rigidly-compactly generated tensor triangulated category and $\mathcal {K}$ is a compactly generated triangulated category on which $\mathcal {T}$ acts, in the sense of Stevenson. We prove that if $\rm {Spc}(\mathcal {T}^{c})$ is Noetherian and $\mathcal {K}$ is stable, then each object in $\mathcal {K}$ has a unique functorial tower, filtered by Balmer-Favi cosupports. This is an analogy of Stevenson's work on filtrations by Balmer-Favi supports. (English) |
| Keyword: | triangulated category |
| Keyword: | colocalizing subcategory |
| Keyword: | Balmer-Favi cosupport |
| Keyword: | filtration |
| MSC: | 18D15 |
| MSC: | 18G80 |
| MSC: | 18M05 |
| DOI: | 10.21136/CMJ.2025.0018-25 |
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| Date available: | 2025-09-19T12:05:38Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153064 |
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| Reference: | [2] Balmer, P., Favi, G.: Generalized tensor idempotents and the telescope conjecture.Proc. Lond. Math. Soc. (3) 102 (2011), 1161-1185. Zbl 1220.18009, MR 2806103, 10.1112/plms/pdq050 |
| Reference: | [3] Barthel, T., Castellana, N., Heard, D., Sanders, B.: Cosupport in tensor triangular geometry.Available at https://arxiv.org/abs/2303.13480 (2023), 87 pages. 10.48550/arXiv.2303.13480 |
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| Reference: | [7] Benson, D. J., Iyengar, S. B., Krause, H.: Colocalizing subcategories and cosupport.J. Reine Angew. Math. 673 (2012), 161-207. Zbl 1271.18012, MR 2999131, 10.1515/CRELLE.2011.180 |
| Reference: | [8] Neeman, A.: Colocalizing subcategories of $\Bbb D(R)$.J. Reine Angew. Math. 653 (2011), 221-243. Zbl 1221.13030, MR 2794632, 10.1515/crelle.2011.028 |
| Reference: | [9] Stevenson, G.: Support theory via actions of tensor triangulated categories.J. Reine Angew. Math. 681 (2013), 219-254. Zbl 1280.18010, MR 3181496, 10.1515/crelle-2012-0025 |
| Reference: | [10] Stevenson, G.: Subcategories of singularity categories via tensor actions.Compos. Math. 150 (2014), 229-272. Zbl 1322.18004, MR 3177268, 10.1112/S0010437X1300746X |
| Reference: | [11] Stevenson, G.: Filtrations via tensor actions.Int. Math. Res. Not. 2018 (2018), 2535-2558. Zbl 1410.18015, MR 3801492, 10.1093/imrn/rnw325 |
| Reference: | [12] Verasdanis, C.: Costratification and actions of tensor-triangulated categories.Available at https://arxiv.org/abs/2211.04139 (2022), 27 pages. 10.48550/arXiv.2211.04139 |
| Reference: | [13] Verasdanis, C.: Colocalizing subcategories of singularity categories.J. Algebra 662 (2025), 608-624. Zbl 1551.18020, MR 4795668, 10.1016/j.jalgebra.2024.08.029 |
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