Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908910087045120 |
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| author | Svoray, Yotam |
| author_facet | Svoray, Yotam |
| contents | This paper develops a theory of isolated hypersurface singularities in mixed characteristic $(0,p)$, focusing on quotient rings over a Discrete Valuation Ring (DVR). We introduce and study analogues of the classical Tjurina and Milnor numbers for this setting, prove a generalized analogue of the determinacy theorem and the Mather-Yau Theorem for complete Noetherian local rings, and define numerical invariants that provide distinct criteria for detecting isolated singularities in the unramified and ramified cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings Svoray, Yotam Commutative Algebra Algebraic Geometry This paper develops a theory of isolated hypersurface singularities in mixed characteristic $(0,p)$, focusing on quotient rings over a Discrete Valuation Ring (DVR). We introduce and study analogues of the classical Tjurina and Milnor numbers for this setting, prove a generalized analogue of the determinacy theorem and the Mather-Yau Theorem for complete Noetherian local rings, and define numerical invariants that provide distinct criteria for detecting isolated singularities in the unramified and ramified cases. |
| title | Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2512.18506 |