{
  "id": "math/0610694",
  "version": "v1",
  "published": "2006-10-23T18:32:53.000Z",
  "updated": "2006-10-23T18:32:53.000Z",
  "title": "On anticyclotomic mu-invariants of modular forms",
  "authors": [
    "Robert Pollack",
    "Tom Weston"
  ],
  "doi": "10.1112/S0010437X11005318",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let f be a modular form of weight 2 and trivial character. Fix also an imaginary quadratic field K. We use work of Bertolini-Darmon and Vatsal to study the mu-invariant of the p-adic Selmer group of f over the anticyclotomic Zp-extension of K. In particular, we verify the mu-part of the main conjecture in this context. The proof of this result is based on an analysis of congruences of modular forms, leading to a conjectural quantitative version of level-lowering (which we verify in the case that Mazur's principle applies).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-23T18:32:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F33",
      "11G05"
    ],
    "keywords": [
      "modular form",
      "anticyclotomic mu-invariants",
      "imaginary quadratic field",
      "p-adic selmer group",
      "mazurs principle applies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10694P"
    }
  }
}