{
  "annotation_id": "9fd2e5df-59b7-4b9a-a6e3-a3553e88e5e9",
  "date_created": "2026-02-17T05:53:24.271000Z",
  "date_modified": "2026-02-17T05:53:24.271000Z",
  "file_hash": "5b534d61ce35502bf94e5dcd1ada1099febdc366db85380a01bd637b98ef57d7",
  "private": false,
  "record": {
    "abstract": "Let $C$ be a smooth projective curve over an algebraically closed field ${\\mathbb{F}}$ equipped with the action of a finite group $G$. When $p =\\textrm{char}(\\mathbb{F})$ divides the order of $G$, the long-standing problem of computing the induced representation of $G$ on the space $H^0(C,\\Omega^{\\otimes m}_C)$ of globally holomorphic polydifferentials remains unsolved in general. In this paper, we study the case of the group $G = \\mathrm{SL}_2(\\mathbb{F}_q)$ (where $q$ is a power of~$p$) acting on the Drinfeld curve $C$ which is the projective plane curve given by the equation $XY^q-X^qY-Z^{q+1} = 0$. When $q = p$, we fully decompose $H^0(C,\\Omega^{\\otimes m}_C)$ as a direct sum of indecomposable $\\mathbb{F}[G]$-modules. For arbitrary $q$, we give a partial decomposition in terms of an explicit $\\mathbb{F}$-basis of $H^0(C,\\Omega^{\\otimes m}_C)$.",
    "arxiv_id": "2601.09956",
    "authors": [
      "Denver-James Logan Marchment",
      "Bernhard K\u00f6ck"
    ],
    "categories": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The Galois Structure of the Spaces of polydifferentials on the Drinfeld Curve",
    "url": "https://arxiv.org/abs/2601.09956",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ba4fba5a-7914-40eb-ad86-70958b5373c9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}