{"title":"Diophantine stability for curves over finite fields","authors":"Francesc Bars, Joan Carles Lario","doi":"arxiv-2409.07086","DOIUrl":null,"url":null,"abstract":"We carry out a survey on curves defined over finite fields that are\nDiophantine stable; that is, with the property that the set of points of the\ncurve is not altered under a proper field extension. First, we derive some\ngeneral results of such curves and then we analyze several families of curves\nthat happen to be Diophantine stable.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07086","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We carry out a survey on curves defined over finite fields that are
Diophantine stable; that is, with the property that the set of points of the
curve is not altered under a proper field extension. First, we derive some
general results of such curves and then we analyze several families of curves
that happen to be Diophantine stable.
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