{"title":"关于全局行列式方法","authors":"Chunhui LIU","doi":"10.24033/bsmf.2859","DOIUrl":null,"url":null,"abstract":"In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also explain why some constants will be more explicit if we admit the Generalized Riemann Hypothesis.","PeriodicalId":55332,"journal":{"name":"Bulletin De La Societe Mathematique De France","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the global determinant method\",\"authors\":\"Chunhui LIU\",\"doi\":\"10.24033/bsmf.2859\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also explain why some constants will be more explicit if we admit the Generalized Riemann Hypothesis.\",\"PeriodicalId\":55332,\"journal\":{\"name\":\"Bulletin De La Societe Mathematique De France\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin De La Societe Mathematique De France\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24033/bsmf.2859\",\"RegionNum\":4,\"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":"Bulletin De La Societe Mathematique De France","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24033/bsmf.2859","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we build the global determinant method of Salberger by Arakelov geometry explicitly. As an application, we study the dependence on the degree of the number of rational points of bounded height in plane curves. We will also explain why some constants will be more explicit if we admit the Generalized Riemann Hypothesis.
期刊介绍：
The Bulletin de la Société Mathématique de France was founded in 1873, and it has published works by some of the most prestigious mathematicians, including for example H. Poincaré, E. Borel, E. Cartan, A. Grothendieck and J. Leray. It continues to be a journal of the highest mathematical quality, using a rigorous refereeing process, as well as a discerning selection procedure. Its editorial board members have diverse specializations in mathematics, ensuring that articles in all areas of mathematics are considered. Promising work by young authors is encouraged.
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