{
  "abstract": "We study $\\mathbf{E}_n$-algebras with ramification in their $π_0$ and in particular show that the existence of ramification places strong limitations on their chromatic behavior. In particular, we show that $π_0$ of nonzero $K(1)$-local $\\mathbf{E}_4$-$\\mathrm{KU}$-algebras cannot have a map from the ring of integers in a ramified extension of $\\mathbf{Q}_p$, and we show that a $p$-complete $\\mathbf{E}_2$-ring with a map from a perfectoid ring into its $π_0$ is an associative $\\mathbf{Z}_p$-algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33754",
  "author_total": 2,
  "authors": [
    {
      "name": "Sanath K. Devalapurkar"
    },
    {
      "name": "Ishan Levy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f53sybcfattwv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33754",
  "fulltext_url": null,
  "id": "f53sybcfattwv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33754",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  ],
  "openalex": "W7223874507",
  "pdf_url": "https://arxiv.org/pdf/2610.33754",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f53sybcfattwv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33754",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33754"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Ramification in $\\mathbf{E}_{n}$-algebras",
  "title_text": "Ramification in E_n-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/f53sybcfattwv",
  "venue": "arXiv",
  "versions": []
}