{
  "id": "2210.08200",
  "version": "v1",
  "published": "2022-10-15T05:17:50.000Z",
  "updated": "2022-10-15T05:17:50.000Z",
  "title": "On ${\\mathrm{Ext}}^1$ for Drinfeld modules",
  "authors": [
    "D. E. Kedzierski",
    "P. Krasoń"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A={\\mathbb F}_q[t]$ be the polynomial ring over a finite field ${\\mathbb F}_q$ and let $\\phi $ and $\\psi$ be $A-$Drinfeld modules. In this paper we consider the group ${\\mathrm{Ext}}^1(\\phi ,\\psi )$ with the Baer addition. We show that if $\\mathrm{rank}\\phi >\\mathrm{rank}\\psi$ then $\\mathrm{Ext^1}(\\phi,\\psi)$ has the structure of a \\tm module. We give complete formulas describing this structure. We also establish duality between Ext groups for t-modules and the corresponding adjoint ${t}^{\\sigma}$-modules. Finally, we prove the existence of \"Hom-Ext\"$ six-term exact sequences for \\tm modules. As the category of t- modules is only additive (not abelian) this result is nontrivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-15T05:17:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09"
    ],
    "keywords": [
      "drinfeld modules",
      "six-term exact sequences",
      "finite field",
      "ext groups",
      "baer addition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}