{"title":"简单无性变上的线性独立性","authors":"Duc Hiep Pham","doi":"10.1007/s10998-024-00573-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish new results on complex and <i>p</i>-adic linear independence on general simple abelian varieties defined over the field of algebraic numbers <span>\\(\\overline{{\\mathbb {Q}}}\\)</span>. In particular, these results extend some previous results on that concerning elliptic curves and simple abelian varieties with complex multiplication defined over <span>\\(\\overline{{\\mathbb {Q}}}\\)</span>.</p>","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"68 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear independence on simple abelian varieties\",\"authors\":\"Duc Hiep Pham\",\"doi\":\"10.1007/s10998-024-00573-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we establish new results on complex and <i>p</i>-adic linear independence on general simple abelian varieties defined over the field of algebraic numbers <span>\\\\(\\\\overline{{\\\\mathbb {Q}}}\\\\)</span>. In particular, these results extend some previous results on that concerning elliptic curves and simple abelian varieties with complex multiplication defined over <span>\\\\(\\\\overline{{\\\\mathbb {Q}}}\\\\)</span>.</p>\",\"PeriodicalId\":49706,\"journal\":{\"name\":\"Periodica Mathematica Hungarica\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Periodica Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10998-024-00573-6\",\"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":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00573-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we establish new results on complex and p-adic linear independence on general simple abelian varieties defined over the field of algebraic numbers \(\overline{{\mathbb {Q}}}\). In particular, these results extend some previous results on that concerning elliptic curves and simple abelian varieties with complex multiplication defined over \(\overline{{\mathbb {Q}}}\).
期刊介绍:
Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica.
Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.