{
  "annotation_id": "f7bf61a9-1a24-4bd8-97cd-1f31fbc775c3",
  "date_created": "2026-02-17T05:53:24.412000Z",
  "date_modified": "2026-02-17T05:53:24.412000Z",
  "file_hash": "136ae3597d0dd1de3266613ea34696acb68fa37c3c4c8f794f3054d500bf580c",
  "private": false,
  "record": {
    "abstract": "In this paper we obtain several results related to the $p$-adic interpolation of the classical Cogdell lift, mapping special cycles on Picard modular surfaces to elliptic modular forms. The results have a three-fold nature: in the first part of the paper, we $p$-adically interpolate the adjoint Kudla lift, exploiting the previously constructed $\\Lambda$-adic Kudla lift. In the second part, we construct higher weight cycles in Kuga-Sato varieties attached to Picard modular surfaces, and show modularity of the generating series of these cycles, thus obtaining a higher weight analogue of the Cogdell lift. Finally, we apply the formalism introduced by Loeffler to construct $p$-adic analytic cohomology classes of special cycles, whose generating series is proved to be a Hida family interpolating the Cogdell lifts in the weight and level variables.",
    "arxiv_id": "2601.10077",
    "authors": [
      "Francesco Maria Iudica"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "A $p$-adic interpolation of the Cogdell lift",
    "url": "https://arxiv.org/abs/2601.10077",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "34b70a3b-c547-43c7-b703-3a1411f3b73a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}