Classifying smashing ideals in derived categories of valuation domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910529574928384 |
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| author | Balchin, Scott Tecklenburg, Florian |
| author_facet | Balchin, Scott Tecklenburg, Florian |
| contents | Building on results of Bazzoni-Šťov\'ıček, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying smashing ideals in derived categories of valuation domains Balchin, Scott Tecklenburg, Florian Commutative Algebra Algebraic Topology Building on results of Bazzoni-Šťov\'ıček, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories. |
| title | Classifying smashing ideals in derived categories of valuation domains |
| topic | Commutative Algebra Algebraic Topology |
| url | https://arxiv.org/abs/2407.11791 |