{
  "id": "2308.04334",
  "version": "v1",
  "published": "2023-08-08T15:28:08.000Z",
  "updated": "2023-08-08T15:28:08.000Z",
  "title": "Some questions arising from the study of cohomology on flag varieties",
  "authors": [
    "Zhao Gao",
    "Claudiu Raicu",
    "Keller VandeBogert"
  ],
  "categories": [
    "math.AG",
    "math.AC",
    "math.RT"
  ],
  "abstract": "A fundamental problem at the confluence of algebraic geometry and representation theory is to describe the cohomology of line bundles on flag varieties over a field of characteristic p. When p=0, the solution is given by the celebrated Borel-Weil-Bott Theorem, while for p>0 the problem is widely open. In this note we describe a collection of open questions that arise from the study of particular cases of the general theory, focusing on their combinatorial and commutative algebra aspects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-08T15:28:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "20G05",
      "05E05"
    ],
    "keywords": [
      "flag varieties",
      "questions arising",
      "cohomology",
      "fundamental problem",
      "algebraic geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}