{
  "abstract": "We develop a plus and minus Iwasawa theory for CM elliptic curves with potentially supersingular reduction at a prime $p\\ge5$. 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 $\\mathbb{Z}_p$-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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13063",
  "author_total": 2,
  "authors": [
    {
      "name": "Ben Forrás"
    },
    {
      "name": "Antonio Lei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vwg4tkaajy2j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13063",
  "fulltext_url": null,
  "id": "1vwg4tkaajy2j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13063",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213072463",
  "pdf_url": "https://arxiv.org/pdf/2609.13063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vwg4tkaajy2j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Iwasawa theory of CM elliptic curves at potentially supersingular primes",
  "title_text": "Iwasawa theory of CM elliptic curves at potentially supersingular primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/1vwg4tkaajy2j",
  "venue": "arXiv",
  "versions": []
}