Uniqueness of dg enhancements for the derived category of a Grothendieck category

  • Alberto Canonaco

    Università degli Studi di Pavia, Italy
  • Paolo Stellari

    Università degli Studi di Milano, Italy

Abstract

We prove that the derived category of a Grothendieck abelian category has a unique dg enhancement. Under some additional assumptions, we show that the same result holds true for its subcategory of compact objects. As a consequence, we deduce that the unbounded derived category of quasi-coherent sheaves on an algebraic stack and the category of perfect complexes on a noetherian concentrated algebraic stack with quasi-finite affine diagonal and enough perfect coherent sheaves have a unique dg enhancement. In particular, the category of perfect complexes on a noetherian scheme with enough locally free sheaves has a unique dg enhancement.

Cite this article

Alberto Canonaco, Paolo Stellari, Uniqueness of dg enhancements for the derived category of a Grothendieck category. J. Eur. Math. Soc. 20 (2018), no. 11, pp. 2607–2641

DOI 10.4171/JEMS/820