{
  "annotation_id": "28bc9b62-3b1c-4466-af76-3929a93999b1",
  "date_created": "2026-02-17T05:53:23.349000Z",
  "date_modified": "2026-02-17T05:53:23.349000Z",
  "file_hash": "6ae420e32cbc9da960db4a498da3214b5aba363cc1d48c88b8bda0a7b02eb586",
  "private": false,
  "record": {
    "abstract": "Let $X$ be a smooth projective variety over an arbitrary field $k$ of characteristic zero. We explore infinitesimal deformations of the Chow group $CH^{p}(X)$ via its formal completion $\\widehat{CH}^{p}$, a functor defined on the category of local augmented Artinian $k$-algebras. Under a natural vanishing condition on Hodge cohomology groups, for certain augmented graded Artinian $k$-algebras $A$ with the maximal ideal $m_{A}$, we prove that \\[ \\widehat{CH}^{p}(A) \\cong H^{p}(X, \\Omega^{p-1}_{X/ k})\\otimes_{k}m_{A}. \\]This extends earlier results of Bloch and others from the case where $k$ is algebraic over $\\mathbb{Q}$ to arbitrary fields of characteristic zero,and gives a partial affirmative answer to a general question linking the pro-representability of Chow groups to a specific set of Hodge-theoretic vanishing conditions.",
    "arxiv_id": "2601.10309",
    "authors": [
      "Sen Yang"
    ],
    "categories": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "title": "Deformations of Chow groups via cyclic homology",
    "url": "https://arxiv.org/abs/2601.10309",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d49b9f6d-5295-45af-b301-4877fc63fd35",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}