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We investigate the asymptotic behavior of the p-part of the Tate-Shafarevich group of a CM elliptic curve over the anticyclotomic \(\mathbb {Z}_p\) -extension of the CM field at inert primes \(p\ge 5\) . A key tool of the proof is our recent work on anticyclotomic CM Iwasawa theory at inert primes.

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On the Tate-Shafarevich Groups of CM Elliptic Curves Over Anticyclotomic \(\mathbb {Z}_p\) -Extensions at Inert Primes

  • 会议论文

  • 发表日期：

    2026年

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  • Ashay A. Burungale,
  • Shinichi Kobayashi,
  • Kazuto Ota

摘要

We investigate the asymptotic behavior of the p-part of the Tate-Shafarevich group of a CM elliptic curve over the anticyclotomic \(\mathbb {Z}_p\) -extension of the CM field at inert primes \(p\ge 5\) . A key tool of the proof is our recent work on anticyclotomic CM Iwasawa theory at inert primes.