{
  "id": "math/0508608",
  "version": "v1",
  "published": "2005-08-30T17:41:01.000Z",
  "updated": "2005-08-30T17:41:01.000Z",
  "title": "Kida's formula and congruences",
  "authors": [
    "Robert Pollack",
    "Tom Weston"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian p-extension of Q to its p-adic Iwasawa invariants over Q. On the algebraic side our methods, which make use of congruences between modular forms, yield a Kida-type formula for a very general class of ordinary Galois representations. We are further able to deduce a Kida-type formula for elliptic curves at supersingular primes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-30T17:41:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11F33",
      "11F80"
    ],
    "keywords": [
      "kidas formula",
      "congruences",
      "algebraic p-adic iwasawa invariants",
      "elliptic curves",
      "kida-type formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8608P"
    }
  }
}