{
  "id": "2104.13407",
  "version": "v1",
  "published": "2021-04-27T18:07:26.000Z",
  "updated": "2021-04-27T18:07:26.000Z",
  "title": "Constructing and calculating Adams operations on topological modular forms",
  "authors": [
    "Jack Morgan Davies"
  ],
  "comment": "43 pages, comments always welcome",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "We construct stable Adams operations on the cohomology theory Tmf of topological modular forms. This is done by extending the sheaf defining Tmf to be functorial with respect to isogenies of generalised elliptic curves of invertible degree. These Adams operations are then calculated on the homotopy groups of Tmf using a combination of descent spectral sequences, the theory of synthetic spectra, and Anderson duality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T18:07:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N34",
      "55N22",
      "55S25",
      "55P43",
      "11F23",
      "14F20"
    ],
    "keywords": [
      "topological modular forms",
      "calculating adams operations",
      "construct stable adams operations",
      "descent spectral sequences",
      "cohomology theory tmf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}