{
  "id": "2502.05421",
  "version": "v1",
  "published": "2025-02-08T03:13:57.000Z",
  "updated": "2025-02-08T03:13:57.000Z",
  "title": "Slopes and weights of $\\ell$-adic cohomology of rigid spaces",
  "authors": [
    "Qing Lu",
    "Weizhe Zheng"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We prove that Frobenius eigenvalues of $\\ell$-adic cohomology and $\\ell$-adic intersection cohomology of rigid spaces over $p$-adic local fields are algebraic integers and we give bounds for their $p$-adic valuations. As an application, we deduce bounds for their weights, proving conjectures of Bhatt, Hansen, and Zavyalov. We also give examples of monodromy-pure perverse sheaves on projective curves with non monodromy-pure cohomology, answering a question of Hansen and Zavyalov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-08T03:13:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F20",
      "14G22"
    ],
    "keywords": [
      "adic cohomology",
      "rigid spaces",
      "non monodromy-pure cohomology",
      "adic intersection cohomology",
      "adic local fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}