{
  "id": "1103.1235",
  "version": "v3",
  "published": "2011-03-07T11:01:19.000Z",
  "updated": "2011-06-23T12:35:13.000Z",
  "title": "Reconstructing the spectrum of F_1 from the stable homotopy category",
  "authors": [
    "Stella Anevski"
  ],
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "The finite stable homotopy category S_0 has been suggested as a candidate for a category of perfect complexes over the monoid scheme Spec F_1. We apply a reconstruction theorem from algebraic geometry to S_0, and show that one recovers the one point topological space. We also classify filtering subsets of the set of principal thick subcategories of S_0, and of its p-local versions. This is motivated by a result saying that the analogous classification for the category of perfect complexes over an affine scheme provides topological information.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-06-23T12:35:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18F99"
    ],
    "keywords": [
      "perfect complexes",
      "finite stable homotopy category",
      "monoid scheme spec",
      "principal thick subcategories",
      "algebraic geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1235A"
    }
  }
}