Upper Ramification Groups for Arbitrary Valuation Rings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866929299666239488 |
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| author | Kato, Kazuya Thatte, Vaidehee |
| author_facet | Kato, Kazuya Thatte, Vaidehee |
| contents | T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring $A$ with field of fractions $K$ and for a finite Galois extension $L$ of $K$, the integral closure $B$ of $A$ in $L$ is a filtered union of subrings of $B$ which are of complete intersection over $A$. By this, we can obtain a ramification theory of Henselian valuation rings as the limit of the ramification theory of Saito. Our theory generalizes the ramification theory of complete discrete valuation rings of Abbes-Saito. We study "defect extensions" which are not treated in these previous works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_09832 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Upper Ramification Groups for Arbitrary Valuation Rings Kato, Kazuya Thatte, Vaidehee Number Theory Algebraic Geometry 11G99(Primary) 14G99(Secondary) T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring $A$ with field of fractions $K$ and for a finite Galois extension $L$ of $K$, the integral closure $B$ of $A$ in $L$ is a filtered union of subrings of $B$ which are of complete intersection over $A$. By this, we can obtain a ramification theory of Henselian valuation rings as the limit of the ramification theory of Saito. Our theory generalizes the ramification theory of complete discrete valuation rings of Abbes-Saito. We study "defect extensions" which are not treated in these previous works. |
| title | Upper Ramification Groups for Arbitrary Valuation Rings |
| topic | Number Theory Algebraic Geometry 11G99(Primary) 14G99(Secondary) |
| url | https://arxiv.org/abs/1909.09832 |