Iwasawa main conjecture for Rankin-Selberg p-adic L-functions
文献类型：期刊论文
| 作者 | Wan, Xin1,2 |
| 刊名 | ALGEBRA & NUMBER THEORY
 |
| 出版日期 | 2020 |
| 卷号 | 14期号:2页码:383-483 |
| 关键词 | Iwasawa main conjecture Rankin-Selberg |
| ISSN号 | 1937-0652 |
| DOI | 10.2140/ant.2020.14.383 |
| 英文摘要 | In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa main conjecture for this p-adic L-function. We prove this conjecture using congruences between Klingen-Eisenstein series and cusp forms on the group GU(3, 1), following the strategy of recent work by C. Skinner and E. Urban. The actual argument is, however, more complicated due to the need to work with general Fourier-Jacobi expansions. This theorem is used to deduce a converse of the Gross-Zagier-Kolyvagin theorem and the p-adic part of the precise BSD formula in the rank one case. |
| 资助项目 | Chinese Academy of Science[Y729025EE1] ; NSFC[11688101] ; NSFC[11621061] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000537944500004 |
| 出版者 | MATHEMATICAL SCIENCE PUBL |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51587]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wan, Xin |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 2.Univ Chinese Acad Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Wan, Xin. Iwasawa main conjecture for Rankin-Selberg p-adic L-functions[J]. ALGEBRA & NUMBER THEORY,2020,14(2):383-483. |
| APA | Wan, Xin.(2020).Iwasawa main conjecture for Rankin-Selberg p-adic L-functions.ALGEBRA & NUMBER THEORY,14(2),383-483. |
| MLA | Wan, Xin."Iwasawa main conjecture for Rankin-Selberg p-adic L-functions".ALGEBRA & NUMBER THEORY 14.2(2020):383-483. |
入库方式： OAI收割
来源：数学与系统科学研究院
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