{"title":"超椭圆曲线的常规模型","authors":"Simone Muselli","doi":"10.1016/j.indag.2023.12.001","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>K</mi></math></span> be a complete discretely valued field of residue characteristic not 2 and <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> its ring of integers. We explicitly construct a regular model over <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> with strict normal crossings of any hyperelliptic curve <span><math><mrow><mi>C</mi><mo>/</mo><mi>K</mi><mo>:</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. For this purpose, we introduce the new notion of <em>MacLane cluster picture</em>, that aims to be a link between clusters and MacLane valuations.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0019357723001040/pdfft?md5=04ca296b6016027d47af6c7c64f21d09&pid=1-s2.0-S0019357723001040-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Regular models of hyperelliptic curves\",\"authors\":\"Simone Muselli\",\"doi\":\"10.1016/j.indag.2023.12.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mi>K</mi></math></span> be a complete discretely valued field of residue characteristic not 2 and <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> its ring of integers. We explicitly construct a regular model over <span><math><msub><mrow><mi>O</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> with strict normal crossings of any hyperelliptic curve <span><math><mrow><mi>C</mi><mo>/</mo><mi>K</mi><mo>:</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. For this purpose, we introduce the new notion of <em>MacLane cluster picture</em>, that aims to be a link between clusters and MacLane valuations.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0019357723001040/pdfft?md5=04ca296b6016027d47af6c7c64f21d09&pid=1-s2.0-S0019357723001040-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357723001040\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357723001040","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 K 是残差特征不为 2 的完整离散值域，OK 是其整数环。我们明确地在 OK 上构造了一个具有严格法交叉的任何超椭圆曲线 C/K:y2=f(x) 的正则模型。为此，我们引入了新的麦克莱恩簇图象概念，旨在成为簇与麦克莱恩估值之间的联系。
Let be a complete discretely valued field of residue characteristic not 2 and its ring of integers. We explicitly construct a regular model over with strict normal crossings of any hyperelliptic curve . For this purpose, we introduce the new notion of MacLane cluster picture, that aims to be a link between clusters and MacLane valuations.
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