{
  "id": "1112.1761",
  "version": "v3",
  "published": "2011-12-08T04:03:45.000Z",
  "updated": "2012-08-17T14:19:24.000Z",
  "title": "Tannakization in derived algebraic geometry",
  "authors": [
    "Isamu Iwanari"
  ],
  "comment": "a result added in section 5",
  "categories": [
    "math.AG",
    "math.AT",
    "math.NT"
  ],
  "abstract": "We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be viewed as infinity-categorical generalization of the work of Joyal-Street and Nori. We then apply it to the stable infinity-category of mixed motives equipped with the realization functor of a mixed Weil cohomology and obtain a derived motivic Galois group whose representation category has a universality, and which represents the automorphism group of the realization functor. Also, we present basic properties of derived affine group schemes in Appendix.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-17T14:19:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived algebraic geometry",
      "derived affine group scheme",
      "symmetric monoidal infinity-category",
      "realization functor",
      "representation category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1761I"
    }
  }
}