{
  "id": "1910.12303",
  "version": "v1",
  "published": "2019-10-27T17:19:07.000Z",
  "updated": "2019-10-27T17:19:07.000Z",
  "title": "Finite descent obstruction for Hilbert modular varieties",
  "authors": [
    "Gregorio Baldi",
    "Giada Grossi"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $S$ be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of $\\mathbb{Z}_{S}$-points on integral models of Hilbert modular varieties, extending a result of D.Helm and F.Voloch about modular curves. Let $L$ be a totally real field. Under (a special case of) the absolute Hodge conjecture and a weak Serre's conjecture for mod $\\ell$ representations of the absolute Galois group of $L$, we prove that the same holds also for the $\\mathcal{O}_{L,S}$-points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-27T17:19:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert modular varieties",
      "finite descent obstruction",
      "finite galois descent obstruction",
      "absolute hodge conjecture",
      "weak serres conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}