{
  "abstract": "We recast the theory of power operations in chromatic height $1$ using higher semiadditivity. In particular, we show that if the height $1$ cyclotomic extension of a commutative algebra $R$ is Galois, then power operations on $R$-algebras are exactly $δ$-ring operations. We also show that semiadditive power operations on chromatically localized algebraic $K$-theory agree with power operations defined using polynomial functoriality. As an application, we deduce that the map from the $K$-theory of a $\\mathbb{Q}$-linear symmetric monoidal category to its $K(1)$-localization is a $δ$-ring homomorphism on the level of underlying spaces. It is well known that operations on the $K$-theory of $\\mathbb{Q}$-linear symmetric monoidal categories are $λ$-ring operations, and since $δ$-rings are `$p$-typical' $λ$-rings, this is an instance of the redshift philosophy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34992",
  "author_total": 1,
  "authors": [
    {
      "name": "Beckham Myers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdbac7w4xvgb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34992",
  "fulltext_url": null,
  "id": "fdbac7w4xvgb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34992",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7223959120",
  "pdf_url": "https://arxiv.org/pdf/2610.34992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdbac7w4xvgb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34992"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Semiadditive Power Operations in Chromatic Height $1$",
  "title_text": "Semiadditive Power Operations in Chromatic Height $1$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/fdbac7w4xvgb4",
  "venue": "arXiv",
  "versions": []
}