Geodesic
Uniqueness of dg enhancements for the derived category of a Grothendieck category
Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2607-2641

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/820
Classification : 14-XX, 18-XX
Keywords: Dg categories, dg enhancements, triangulated categories 
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     author = {Alberto Canonaco and Paolo Stellari},
     title = {Uniqueness of dg enhancements for the derived category of a {Grothendieck} category},
     journal = {Journal of the European Mathematical Society},
     pages = {2607--2641},
     publisher = {mathdoc},
     volume = {20},
     number = {11},
     year = {2018},
     doi = {10.4171/jems/820},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/820/}
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Alberto Canonaco; Paolo Stellari. Uniqueness of dg enhancements for the derived category of a Grothendieck category. Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2607-2641. doi: 10.4171/jems/820

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