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

John Coates ^[1] ; Jianing Li ^[2] ; Yongxiong L ^[3]
1. [1] Emmanuel College
  
  Emmanuel College
  
  Estados Unidos
2. [2] University of Science and Technology of China
  
  University of Science and Technology of China
  
  China
3. [3] Tsinghua University
  
  Tsinghua University
  
  China
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 2, 2021
Idioma: inglés
DOI: 10.1007/s00029-021-00644-3
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Resumen
- 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.