{
  "id": "2411.11201",
  "version": "v1",
  "published": "2024-11-17T23:34:59.000Z",
  "updated": "2024-11-17T23:34:59.000Z",
  "title": "An Infinite Family of Artin-Schreier Curves with Minimal a-number",
  "authors": [
    "Iris Y. Shi"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $p$ be an odd prime and $k$ be an algebraically closed field with characteristic $p$. Booher and Cais showed that the $a$-number of a $\\mathbb Z/p \\mathbb Z$-Galois cover of curves $\\phi: Y \\to X$ must be greater than a lower bound determined by the ramification of $\\phi$. In this paper, we provide evidence that the lower bound is optimal by finding examples of Artin-Schreier curves that have $a$-number equal to its lower bound for all $p$. Furthermore we use formal patching to generate infinite families of Artin-Schreier curves with $a$-number equal to the lower bound in any characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-17T23:34:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "artin-schreier curves",
      "infinite family",
      "lower bound",
      "minimal a-number",
      "number equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}