{
  "id": "1402.2617",
  "version": "v2",
  "published": "2014-02-11T20:08:28.000Z",
  "updated": "2015-01-06T09:24:35.000Z",
  "title": "Around conjectures of N. Kuhn",
  "authors": [
    "Nguyen The Cuong",
    "Gérald Gaudens",
    "Powell Geoffrey",
    "Lionel Schwartz"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod $p$ singular cohomology of a space, for $p$ a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes' mapping space theorem. The second (for the prime $2$) is based on an analysis of the $-1$ and $-2$ columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between $\\Fp$-vector spaces. The second result in particular exhibits the power of the functorial approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-11T20:08:28.000Z",
      "abstract": "The following note discuss two ways to extend conjectures of N. Kuhn about the non realization of certain unstable algebras as the mod p singular cohomology of spaces. The first case (established for all primes p) extends and refines preceding work the second and the third author [GS13]. The second one (only for the prime 2) discuss another approach, not depending on Lannes' mapping space theorem and relies on an analysis of the columns -1 and -2 of the Eilenberg-Moore spectral sequence, and the triviality of the associated extension in the category of unstable modules. In both case the statements and proofs will use the links between the categories of unstable modules and functors. In both cases it would be possible to work entirely within the category of unstable modules, however it is much more cleaner and efficient to use both categories, thus this note is propaganda for this point of view.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Nguyen The Cuong",
        "gérald gaudens",
        "Lionel Schwartz"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-01-06T09:24:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unstable modules",
      "eilenberg-moore spectral sequence",
      "mapping space theorem",
      "first case",
      "refines preceding work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.2617C"
    }
  }
}