{
  "id": "1708.06106",
  "version": "v1",
  "published": "2017-08-21T07:41:58.000Z",
  "updated": "2017-08-21T07:41:58.000Z",
  "title": "Regularity of quotients of Drinfeld modular schemes",
  "authors": [
    "Satoshi Kondo",
    "Seidai Yasuda"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be the coordinate ring of a projective smooth curve over a finite field minus a closed point. For a nontrivial ideal $I \\subset A$, Drinfeld defined the notion of structure of level $I$ on a Drinfeld module. We extend this to that of level $N$, where $N$ is a finitely generated torsion $A$-module. The case where $N=(I^{-1}/A)^d$, where $d$ is the rank of the Drinfeld module,coincides with the structure of level $I$. The moduli functor is representable by a regular affine scheme. The automorphism group $\\mathrm{Aut}_{A}(N)$ acts on the moduli space. Our theorem gives a class of subgroups for which the quotient of the moduli scheme is regular. Examples include generalizations of $\\Gamma_0$ and of $\\Gamma_1$. We also show that parabolic subgroups appearing in the definition of Hecke correspondences are such subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-21T07:41:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "drinfeld modular schemes",
      "regularity",
      "drinfeld module",
      "finite field minus",
      "regular affine scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}