{
  "abstract": "We study anticyclotomic Iwasawa theory for self-dual twists of $p$-ordinary modular forms of weight two with nebentype $ε^2$, where $ε$ is a non-trivial Dirichlet character of conductor $p$. Under a generalized Heegner hypothesis and suitable residual hypotheses, we prove one divisibility in the anticyclotomic main conjecture in both the definite and indefinite settings. The prime $p$ may split, remain inert, or ramify in the imaginary quadratic field. Our proofs use a compatible bipartite Euler system of Heegner classes and theta elements, together with a comparison with the $p$-adic $L$-functions of Kohen--Pacetti. In the definite case, we prove cotorsion of the Selmer group and the characteristic-ideal divisibility by the $p$-adic $L$-function. In the indefinite case, we prove a rank-one statement and the corresponding divisibility in terms of the Heegner class. We also discuss criteria for equality and their relation to Kolyvagin's conjecture. Specialization gives finite-level Bloch--Kato Selmer bounds with local terms, and applications to Mordell--Weil ranks and $p$-primary Tate--Shafarevich groups for elliptic curves that have potentially ordinary reduction at $p$ satisfying our hypotheses.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03195",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Lei"
    },
    {
      "name": "Peter Neamti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/45p18ptrmgdk8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03195",
  "fulltext_url": null,
  "id": "45p18ptrmgdk8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03195",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/45p18ptrmgdk8.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03195"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Anticyclotomic Iwasawa theory at potentially ordinary primes",
  "title_text": "Anticyclotomic Iwasawa theory at potentially ordinary primes",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:12Z",
  "url": "https://research.draconitic.com/paper/45p18ptrmgdk8",
  "venue": "arXiv",
  "versions": []
}