{
  "id": "1811.08642",
  "version": "v2",
  "published": "2018-11-21T09:09:46.000Z",
  "updated": "2022-02-10T20:54:30.000Z",
  "title": "Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces",
  "authors": [
    "David Chataur",
    "Joana Cirici"
  ],
  "comment": "To appear in Transactions of the American Mathematical Society",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its E-infinity structure. This naturally extends the theory of mixed Hodge structures in rational homotopy to p-adic homotopy theory. The spectral sequence associated to the weight filtration gives a new family of multiplicative algebraic invariants of the varieties for any coefficient ring, carrying Steenrod operations. As a second application, we promote Deligne's intersection complex computing intersection cohomology, to a sheaf carrying E-infinity structures. This allows for a natural interpretation of the Steenrod operations defined on the intersection cohomology of any topological pseudomanifold.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-10T20:54:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N33",
      "32S35"
    ],
    "keywords": [
      "algebraic variety",
      "e-infinity algebra",
      "singular spaces",
      "complex computing intersection cohomology",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}