{"title":"算术方案的Hilbert性质","authors":"Cedric Luger","doi":"10.4064/aa211214-16-11","DOIUrl":null,"url":null,"abstract":"We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite \\'{e}tale covers of arithmetic schemes with the Hilbert property.","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Hilbert property for arithmetic schemes\",\"authors\":\"Cedric Luger\",\"doi\":\"10.4064/aa211214-16-11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite \\\\'{e}tale covers of arithmetic schemes with the Hilbert property.\",\"PeriodicalId\":37888,\"journal\":{\"name\":\"Acta Arithmetica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-12-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Arithmetica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/aa211214-16-11\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Arithmetica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/aa211214-16-11","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We extend the usual Hilbert property for varieties over fields to arithmetic schemes over integral domains by demanding the set of near-integral points (as defined by Vojta) to be non-thin. We then generalize results of Bary-Soroker-Fehm-Petersen and Corvaja-Zannier by proving several structure results related to products and finite \'{e}tale covers of arithmetic schemes with the Hilbert property.
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