Valuation rings of dimension one as limits of smooth algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866913706790617088 |
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| author | Popescu, Dorin |
| author_facet | Popescu, Dorin |
| contents | As in Zariski's Uniformization Theorem we show that a valuation ring $V$ of characteristic $p>0$ of dimension one is a filtered direct limit of smooth ${\bf F}_p$-algebras under some conditions of transcendence degree. Under mild conditions, the algebraic immediate extensions of valuation rings are dense if they are filtered direct limit of smooth morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_08972 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Valuation rings of dimension one as limits of smooth algebras Popescu, Dorin Commutative Algebra Algebraic Geometry As in Zariski's Uniformization Theorem we show that a valuation ring $V$ of characteristic $p>0$ of dimension one is a filtered direct limit of smooth ${\bf F}_p$-algebras under some conditions of transcendence degree. Under mild conditions, the algebraic immediate extensions of valuation rings are dense if they are filtered direct limit of smooth morphisms. |
| title | Valuation rings of dimension one as limits of smooth algebras |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2006.08972 |