p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
文献类型：期刊论文
| 作者 | Burungale, Ashay A.1; Tian, Ye2,3 |
| 刊名 | INVENTIONES MATHEMATICAE
 |
| 出版日期 | 2019-11-02 |
| 页码 | 43 |
| ISSN号 | 0020-9910 |
| DOI | 10.1007/s00222-019-00929-7 |
| 英文摘要 | Let E be a CM elliptic curve over the rationals and p>3-Selmer group Selp infinity(E/Q) and the complex L-function L(s,E/Q). In particular, the Tate-Shafarevich group X(E/Q) is finite whenever corankZpSelp infinity(E/Q)=1. We also prove an analogous p-converse for CM abelian varieties arising from weight two elliptic CM modular forms with trivial central character. For non-CM elliptic curves over the rationals, first general results towards such a p-converse theorem are independently due to Skinner (A converse to a theorem of Gross, Zagier and Kolyvagin, , 2014) and Zhang (Camb J Math 2(2):191-253, 2014). |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000493674500001 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50699]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Burungale, Ashay A. |
| 作者单位 | 1.CALTECH, 1200 E Calif Blvd, Pasadena, CA 91125 USA 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, HLM, MCM, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Burungale, Ashay A.,Tian, Ye. p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin[J]. INVENTIONES MATHEMATICAE,2019:43. |
| APA | Burungale, Ashay A.,&Tian, Ye.(2019).p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin.INVENTIONES MATHEMATICAE,43. |
| MLA | Burungale, Ashay A.,et al."p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin".INVENTIONES MATHEMATICAE (2019):43. |
入库方式： OAI收割
来源：数学与系统科学研究院
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