{
  "id": "1511.03784",
  "version": "v1",
  "published": "2015-11-12T05:49:56.000Z",
  "updated": "2015-11-12T05:49:56.000Z",
  "title": "Computation of the classifying ring of formal groups with complex multiplication",
  "authors": [
    "A. Salch"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.AT"
  ],
  "abstract": "Machinery is developed for computing the classifying ring $L^A$ of one-dimensional formal groups with complex multiplication by $A$, for a given commutative ring $A$. The machinery is then applied to compute $L^A$ for various number rings and cyclic group rings $A$. The ring $L^A$ has been computed, for certain choices of $A$, by M. Lazard, V. Drinfeld, and M. Hazewinkel, but in those cases $L^A$ is always isomorphic to a polynomial algebra. In the present paper, $L^A$ is computed in many cases in which it fails to be a polynomial algebra, leading to a qualitatively different moduli theory and a different presentation for the moduli stack of formal $A$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-12T05:49:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex multiplication",
      "classifying ring",
      "computation",
      "polynomial algebra",
      "cyclic group rings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151103784S"
    }
  }
}