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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.06379 |
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| _version_ | 1866908524591710208 |
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| author | Teissier, Bernard |
| author_facet | Teissier, Bernard |
| contents | Let $R$ be a complete equicharacteristic noetherian local domain with an algebraically closed residue field $k$. Let $ν$ be a zero dimensional valuation of rank one centered in $R$ with value group $Φ$. We show that there is a valuation preserving embedding of $R$ in the ring $k[[t^{Φ_{\geq 0}}]]$ of Hahn series. The method relies on torific local uniformization for rational valuations with finitely generated semigroup and the approximation of rational valuations by semivaluations with finitely generated semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Kaplansky's Embedding Theorem Teissier, Bernard Commutative Algebra Algebraic Geometry Let $R$ be a complete equicharacteristic noetherian local domain with an algebraically closed residue field $k$. Let $ν$ be a zero dimensional valuation of rank one centered in $R$ with value group $Φ$. We show that there is a valuation preserving embedding of $R$ in the ring $k[[t^{Φ_{\geq 0}}]]$ of Hahn series. The method relies on torific local uniformization for rational valuations with finitely generated semigroup and the approximation of rational valuations by semivaluations with finitely generated semigroup. |
| title | On Kaplansky's Embedding Theorem |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2509.06379 |