{"title":"Diophantine 稳定性和二阶项","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":"{\"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}","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}
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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