{"title":"关于完全交叉点的哈塞原理","authors":"Matthew Northey, Pankaj Vishe","doi":"10.1112/s0010437x23007698","DOIUrl":null,"url":null,"abstract":"<p>We prove the Hasse principle for a smooth projective variety <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$X\\subset \\mathbb {P}^{n-1}_\\mathbb {Q}$</span></span></img></span></span> defined by a system of two cubic forms <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$F,G$</span></span></img></span></span> as long as <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$n\\geq 39$</span></span></img></span></span>. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$\\mathbb {Q}$</span></span></img></span></span>.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Hasse principle for complete intersections\",\"authors\":\"Matthew Northey, Pankaj Vishe\",\"doi\":\"10.1112/s0010437x23007698\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove the Hasse principle for a smooth projective variety <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$X\\\\subset \\\\mathbb {P}^{n-1}_\\\\mathbb {Q}$</span></span></img></span></span> defined by a system of two cubic forms <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$F,G$</span></span></img></span></span> as long as <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline3.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$n\\\\geq 39$</span></span></img></span></span>. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304180407639-0000:S0010437X23007698:S0010437X23007698_inline4.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\mathbb {Q}$</span></span></img></span></span>.</p>\",\"PeriodicalId\":55232,\"journal\":{\"name\":\"Compositio Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Compositio Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1112/s0010437x23007698\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Compositio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1112/s0010437x23007698","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove the Hasse principle for a smooth projective variety $X\subset \mathbb {P}^{n-1}_\mathbb {Q}$ defined by a system of two cubic forms $F,G$ as long as $n\geq 39$. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over $\mathbb {Q}$.
期刊介绍：
Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
$X\subset \mathbb {P}^{n-1}_\mathbb {Q}$ defined by a system of two cubic forms 
$F,G$ as long as 
$n\geq 39$. The main tool here is the development of a version of Kloosterman refinement for a smooth system of equations defined over 
$\mathbb {Q}$.
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