{"title":"p-adic 曲线函数域相似性的局部-全局原理","authors":"Jack Barlow","doi":"10.1016/j.jalgebra.2024.08.038","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>p</mi><mo>∈</mo><mi>N</mi></math></span> be a prime with <span><math><mi>p</mi><mo>≠</mo><mn>2</mn></math></span>, and let <em>K</em> be a <em>p</em>-adic field. Let <em>F</em> be the function field of a curve over <em>K</em>. Let <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> be the set of all divisorial discrete valuations of <em>F</em>. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over <em>F</em>. We give a positive answer to this question for a class of adjoint classical groups.</div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A local-global principle for similarities over function fields of p-adic curves\",\"authors\":\"Jack Barlow\",\"doi\":\"10.1016/j.jalgebra.2024.08.038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <span><math><mi>p</mi><mo>∈</mo><mi>N</mi></math></span> be a prime with <span><math><mi>p</mi><mo>≠</mo><mn>2</mn></math></span>, and let <em>K</em> be a <em>p</em>-adic field. Let <em>F</em> be the function field of a curve over <em>K</em>. Let <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> be the set of all divisorial discrete valuations of <em>F</em>. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over <em>F</em>. We give a positive answer to this question for a class of adjoint classical groups.</div></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324005106\",\"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/S0021869324005106","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 p∈N 是一个 p≠2 的素数，设 K 是一个 p-adic 域。让 F 是 K 上曲线的函数域，让 ΩF 是 F 的所有除法离散值的集合。在本文中，我们提出了哈塞原理对于 F 上的半简单邻接线性代数群是否成立的问题，并对一类邻接经典群给出了肯定的答案。
A local-global principle for similarities over function fields of p-adic curves
Let be a prime with , and let K be a p-adic field. Let F be the function field of a curve over K. Let be the set of all divisorial discrete valuations of F. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over F. We give a positive answer to this question for a class of adjoint classical groups.
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