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Iwasawa theory of CM elliptic curves at potentially supersingular primes

  • Ben Forrás
  • Antonio Lei
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Abstract

We develop a plus and minus Iwasawa theory for CM elliptic curves with potentially supersingular reduction at a prime p≥5. We construct local points that satisfy suitable "jumping trace" relations using the Honda--Demchenko theory applied to height-two formal groups over local fields with small ramification degree. These local points allow us to study plus and minus Selmer groups of CM elliptic curves over the cyclotomic ℤp-extension, to construct the corresponding plus and minus p-adic L-functions, and to prove an Iwasawa main conjecture relating these objects. As an application, we obtain asymptotic growth formulae for the p-primary part of the Tate--Shafarevich groups.

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Cite

BibTeXRIS
BibTeX
@misc{forras2026iwasawa,
  title = {{Iwasawa theory of CM elliptic curves at potentially supersingular primes}},
  author = {Ben Forrás and Antonio Lei},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13063},
  eprint = {2609.13063},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13063},
}
RIS
TY  - UNPB
TI  - Iwasawa theory of CM elliptic curves at potentially supersingular primes
AU  - Ben Forrás
AU  - Antonio Lei
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13063
UR  - https://arxiv.org/abs/2609.13063
AB  - We develop a plus and minus Iwasawa theory for CM elliptic curves with potentially supersingular reduction at a prime p≥5. We construct local points that satisfy suitable "jumping trace" relations using the Honda--Demchenko theory applied to height-two formal groups over local fields with small ramification degree. These local points allow us to study plus and minus Selmer groups of CM elliptic curves over the cyclotomic ℤ_p-extension, to construct the corresponding plus and minus p-adic L-functions, and to prove an Iwasawa main conjecture relating these objects. As an application, we obtain asymptotic growth formulae for the p-primary part of the Tate--Shafarevich groups.
ER  -