Non-reduced valuation rings and descent for smooth blowup squares
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916081457692672 |
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| author | Kelly, Shane |
| author_facet | Kelly, Shane |
| contents | We consider a class of non-reduced valuation rings, known in the literature as chain rings. We observe that the Grothendieck topology generated by the Zariski topology and smooth blowup squares is exactly the topology which has chain rings for its local rings, and that sheaves for this topology are \emph{not} characterised by excision for smooth blowup squares. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-reduced valuation rings and descent for smooth blowup squares Kelly, Shane Algebraic Geometry We consider a class of non-reduced valuation rings, known in the literature as chain rings. We observe that the Grothendieck topology generated by the Zariski topology and smooth blowup squares is exactly the topology which has chain rings for its local rings, and that sheaves for this topology are \emph{not} characterised by excision for smooth blowup squares. |
| title | Non-reduced valuation rings and descent for smooth blowup squares |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.02706 |