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Classical Iwasawa theory and infinite descent on a family of abelian varieties

John Coates Emmanuel College, Cambridge, England, UK Jianing Li CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, China Yongxiong Li Yau Mathematical Sciences Center, Tsinghua University, Beijing, China

Number Theory mathscidoc:2204.24002

Selecta Mathematica, 27-28, 2021.4
For primes q≡7 mod 16, the present manuscript shows that elementary methods enable one to prove surprisingly strong results about the Iwasawa theory of the Gross family of elliptic curves with complex multiplication by the ring of integers of the field K=Q(√(-q)), which are in perfect accord with the predictions of the conjecture of Birch and Swinnerton-Dyer. We also prove some interesting phenomena related to a classical conjecture of Greenberg, and give a new proof of an old theorem of Hasse.
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@inproceedings{john2021classical,
  title={Classical Iwasawa theory and infinite descent on a family of abelian varieties},
  author={John Coates, Jianing Li, and Yongxiong Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422143121162277102},
  booktitle={Selecta Mathematica},
  pages={27-28},
  year={2021},
}
John Coates, Jianing Li, and Yongxiong Li. Classical Iwasawa theory and infinite descent on a family of abelian varieties. 2021. In Selecta Mathematica. pp.27-28. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422143121162277102.
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