{
  "id": "2111.11145",
  "version": "v2",
  "published": "2021-11-22T12:10:16.000Z",
  "updated": "2022-11-28T16:38:55.000Z",
  "title": "The strengthened Broué abelian defect group conjecture for ${\\rm SL}(2,p^n)$ and ${\\rm GL}(2,p^n)$",
  "authors": [
    "Xin Huang",
    "Pengcheng Li",
    "Jiping Zhang"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We show that each $p$-block of ${\\rm SL}(2,p^n)$ and ${\\rm GL}(2,p^n)$ over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent, hence give new evidence for a refined version of Brou\\'{e}'s abelian defect group conjecture proposed by Kessar and Linckelmann.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-11-28T16:38:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian defect group conjecture",
      "arbitrary complete discrete valuation ring",
      "splendidly rickard equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}