{
  "annotation_id": "559679c8-e57f-45e3-a066-e1dc598055eb",
  "date_created": "2026-02-17T05:53:11.818000Z",
  "date_modified": "2026-02-17T05:53:11.818000Z",
  "file_hash": "228619a663b7ee2fc79636ae1ad21a88ae95e96efa2b0d3c1878f424edda6987",
  "private": false,
  "record": {
    "abstract": "We introduce coefficient systems of pro-\\\u0027etale motives and pro-\\\u0027etale motivic spectra with coefficients in any condensed ring spectrum and show that they afford the six operations. Over locally \\\u0027etale bounded schemes, \\\u0027etale motivic spectra embed into pro-\\\u0027etale motivic spectra. We then use the framework of condensed category theory to define a solidification process for any $\\widehat{\\mathbb{Z}}$-linear condensed category. Pro-\\\u0027etale motives naturally enhance to a condensed category and we show that their solidification is very close to the category of solid sheaves defined by Fargues-Scholze, suitably modified to work on schemes: this is a rigidity result. As a consequence, we obtain that in contrast with the rigid-analytic setting, solid sheaves on schemes afford the six operations, and we obtain a solid realization functor of motives, extending the $\\ell$-adic realization functor. The solid realization functor is compatible with change of coefficients, which allows one to recover the $\\mathbb{Q}_\\ell$-adic realization functor while remaining in a setting of presentable categories.",
    "arxiv_id": "2601.07358",
    "authors": [
      "Rapha\u00ebl Ruimy",
      "Swann Tubach",
      "Sebastian Wolf"
    ],
    "categories": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Pro-\\\u0027etale motives and solid rigidity",
    "url": "https://arxiv.org/abs/2601.07358",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6e59d06b-9140-4381-9c11-6814ce2ad76a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}