{
  "id": "1608.03795",
  "version": "v1",
  "published": "2016-08-12T14:02:48.000Z",
  "updated": "2016-08-12T14:02:48.000Z",
  "title": "The chromatic splitting conjecture for Noetherian commutative ring spectra",
  "authors": [
    "Tobias Barthel",
    "Drew Heard",
    "Gabriel Valenzuela"
  ],
  "comment": "12 pages. All comments are welcome",
  "categories": [
    "math.AT",
    "math.RT"
  ],
  "abstract": "We formulate a version of Hopkins' chromatic splitting conjecture for an arbitrary structured ring spectrum $R$, and prove it whenever $\\pi_*R$ is Noetherian. Our approach relies on a novel decomposition of the local cohomology functors constructed previously by Benson, Iyengar, and Krause as well as a generalization of Brown--Comenetz duality. As an application, these results provide a new local-to-global principle in the modular representation theory of finite groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-12T14:02:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ring spectrum",
      "chromatic splitting conjecture",
      "noetherian commutative ring spectra",
      "local cohomology functors",
      "modular representation theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}