{
  "annotation_id": "173dc8ca-4c2b-48a4-8aaf-fec3ff035914",
  "date_created": "2026-02-17T05:53:23.668000Z",
  "date_modified": "2026-02-17T05:53:23.668000Z",
  "file_hash": "089d5ac4cd64406a745ea2bd6a6d9058048362902a91ba67b42957c0cd2449b4",
  "private": false,
  "record": {
    "abstract": "We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a broad range of Iwasawa-theoretic scenarios. In particular, our result applies to the triple product of Hida families in both balanced and unbalanced cases, as well as the half-ordinary Rankin-Selberg universal deformations recently studied by the first named author and Loeffler. Our result also significantly generalizes many previously known cases of algebraic functional equations and answers a question of Greenberg.",
    "arxiv_id": "2601.10426",
    "authors": [
      "Zeping Hao",
      "Meng Fai Lim"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Algebraic functional equation for big Galois representations over multiple $\\mathbb{Z}_p$-extensions",
    "url": "https://arxiv.org/abs/2601.10426",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d3f19ac9-5153-4788-a079-f873feb24511",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}