{
  "id": "2305.13074",
  "version": "v1",
  "published": "2023-05-22T14:44:29.000Z",
  "updated": "2023-05-22T14:44:29.000Z",
  "title": "Approximation of the centre of unstable algebras using the nilpotent filtration",
  "authors": [
    "Ouriel Blœdé"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "In a precedent article, we computed the set $\\textbf{C}(K)$ of central elements of an unstable algebra $K$ over the Steenrod algebra, in the sense of Dwyer and Wilkerson, when $K$ is noetherian and $nil_1$-closed. For $K$ noetherian and $k$ a positive integer, we define $\\textbf{C}_k(K)$, the set of so-called central elements of $K$ away from $\\mathcal{N}il_k$ in such a way that, for $K$ $nil_k$-closed, $\\textbf{C}(K)=\\textbf{C}_k(K)$. The sets $\\textbf{C}_k(K)$ are a decreasing filtration, and we describe the obstruction for an element in $\\textbf{C}_k(K)$ to be in $\\textbf{C}_{k+1}(K)$. Since, for $K$ noetherian, $K$ is always $nil_k$-closed for $k$ big enough, this gives us a way to compute the set of central elements of $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-22T14:44:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unstable algebra",
      "nilpotent filtration",
      "central elements",
      "approximation",
      "noetherian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}