{
  "id": "2505.08710",
  "version": "v1",
  "published": "2025-05-13T16:17:49.000Z",
  "updated": "2025-05-13T16:17:49.000Z",
  "title": "On anticyclotomic Euler and Kolyvagin systems",
  "authors": [
    "Luca Mastella",
    "Francesco Zerman"
  ],
  "comment": "36 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce an axiomatization of the notion of ( $p$-complete) anticyclotomic Euler system for a wide class of Galois representations, including those attached to a cuspidal eigenform and to a Hida family of modular forms. Under a minimal set of assumptions, we show how to build from these data a universal Kolyvagin system for the representation and for its anticyclotomic twist. Eventually, we recover some applications to the structure of Selmer groups and Iwasawa main conjectures and we review a few concrete examples of these abstract notions that can be found in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-13T16:17:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11R23"
    ],
    "keywords": [
      "universal kolyvagin system",
      "anticyclotomic euler system",
      "iwasawa main conjectures",
      "cuspidal eigenform",
      "minimal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}