{"title":"Rational points on complete intersections of cubic and quadric hypersurfaces over \n \n \n \n F\n q\n \n \n (\n t\n )\n \n \n $\\mathbb {F}_q(t)$","authors":"Jakob Glas","doi":"10.1112/jlms.12991","DOIUrl":null,"url":null,"abstract":"<p>Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>F</mi>\n <mi>q</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>t</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\mathbb {F}_q(t)$</annotation>\n </semantics></math>, provided <span></span><math>\n <semantics>\n <mrow>\n <mo>char</mo>\n <mo>(</mo>\n <msub>\n <mi>F</mi>\n <mi>q</mi>\n </msub>\n <mo>)</mo>\n <mo>></mo>\n <mn>3</mn>\n </mrow>\n <annotation>$\\operatorname{char}(\\mathbb {F}_q)&gt;3$</annotation>\n </semantics></math>. Under the same hypotheses, we also verify weak approximation.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12991","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12991","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least 23 over , provided . Under the same hypotheses, we also verify weak approximation.
利用德尔塔法的二维版本,我们建立了维数至少为 23 over F q ( t ) $\mathbb {F}_q(t)$,条件为 char ( F q ) > 3 $\operatorname{char}(\mathbb {F}_q)>3$的立方超曲面和二次超曲面的非奇异完全交点上有界高的有理点数的渐近公式。在同样的假设下,我们也验证了弱逼近。
期刊介绍:
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.