{
  "id": "2101.10262",
  "version": "v1",
  "published": "2021-01-25T17:50:10.000Z",
  "updated": "2021-01-25T17:50:10.000Z",
  "title": "Filtered formal groups, Cartier duality, and derived algebraic geometry",
  "authors": [
    "Tasos Moulinos"
  ],
  "comment": "Comments welcome",
  "categories": [
    "math.AG",
    "math.AT",
    "math.KT"
  ],
  "abstract": "We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived algebraic geometry. Applied to the unit section of a formal group $\\widehat{\\mathbb{G}}$, this provides a $\\mathbb{G}_m$-equivariant degeneration of $\\widehat{\\mathbb{G}}$ to its tangent Lie algebra. We prove a unicity result on complete filtrations, which, in particular, identifies the resulting filtration on the coordinate algebra of this deformation with the adic filtration on the coordinate algebra of $\\widehat{\\mathbb{G}}$. We use this in a special case, together with the aforementioned notion of Cartier duality, to recover the filtration on the filtered circle of [MRT19]. Finally, we investigate some properties of $\\widehat{\\mathbb{G}}$-Hochschild homology set out in loc. cit., and describe \"lifts\" of these invariants to the setting of spectral algebraic geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-25T17:50:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived algebraic geometry",
      "filtered formal groups",
      "cartier duality",
      "filtration",
      "coordinate algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}