{"title":"Diophantine stability and second order terms","authors":"Carlo Pagano, Efthymios Sofos","doi":"arxiv-2409.12144","DOIUrl":null,"url":null,"abstract":"We establish a Galois-theoretic trichotomy governing Diophantine stability\nfor genus $0$ curves. We use it to prove that the curve associated to the\nHilbert symbol is Diophantine stable with probability $1$. Our asymptotic\nformula for the second order term exhibits strong bias towards instability.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","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-2409.12144","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 establish a Galois-theoretic trichotomy governing Diophantine stability
for genus $0$ curves. We use it to prove that the curve associated to the
Hilbert symbol is Diophantine stable with probability $1$. Our asymptotic
formula for the second order term exhibits strong bias towards instability.
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