{
  "id": "1510.01915",
  "version": "v1",
  "published": "2015-10-07T12:19:50.000Z",
  "updated": "2015-10-07T12:19:50.000Z",
  "title": "On the exceptional zeros of $p$-non-ordinary $p$-adic $L$-functions and a conjecture of Perrin-Riou",
  "authors": [
    "Denis Benois",
    "Kazim Buyukboduk"
  ],
  "comment": "47 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Our goal in this article is to prove a form of $p$-adic Beilinson formula for the second derivative of the $p$-adic $L$-function associated to a newform $f$ which is non-crystalline semistable at $p$ at its central critical point, by expressing this quantity in terms of a $p$-adic (cyclotomic) regulator defined on an extended trianguline Selmer group. We also prove a two-variable version of this result for height pairings we construct by considering infinitesimal deformations afforded by a Coleman family passing through $f$. This, among other things, leads us to a proof of an appropriate version of Perrin-Riou's conjecture in this set up.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-07T12:19:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional zeros",
      "conjecture",
      "perrin-riou",
      "non-ordinary",
      "extended trianguline selmer group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151001915B"
    }
  }
}