A conjecture on the composition of localizations on a stratified tensor triangulated category
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910831970615296 |
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| author | Bellumat, Nicola |
| author_facet | Bellumat, Nicola |
| contents | We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us general applications to concrete categories examined in mathematical practice. We propose a conjecture which states that the behaviour of the composition of the localizations depends on the chains of inclusions of the Balmer primes indexing said localizations. We prove this conjecture in the case of finite or low dimensional Balmer spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A conjecture on the composition of localizations on a stratified tensor triangulated category Bellumat, Nicola Category Theory Algebraic Topology 18F99 (Primary) 55P60 (Secondary) We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us general applications to concrete categories examined in mathematical practice. We propose a conjecture which states that the behaviour of the composition of the localizations depends on the chains of inclusions of the Balmer primes indexing said localizations. We prove this conjecture in the case of finite or low dimensional Balmer spectra. |
| title | A conjecture on the composition of localizations on a stratified tensor triangulated category |
| topic | Category Theory Algebraic Topology 18F99 (Primary) 55P60 (Secondary) |
| url | https://arxiv.org/abs/2303.01334 |