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
Mots-clés : Dg categories, dg enhancements, triangulated categories 
@article{JEMS_2018_20_11_a1,
     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 = {https://geodesic-test.mathdoc.fr/articles/10.4171/jems/820/}
}
TY  - JOUR
AU  - Alberto Canonaco
AU  - Paolo Stellari
TI  - Uniqueness of dg enhancements for the derived category of a Grothendieck category
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 2607
EP  - 2641
VL  - 20
IS  - 11
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.4171/jems/820/
DO  - 10.4171/jems/820
ID  - JEMS_2018_20_11_a1
ER  - 
%0 Journal Article
%A Alberto Canonaco
%A Paolo Stellari
%T Uniqueness of dg enhancements for the derived category of a Grothendieck category
%J Journal of the European Mathematical Society
%D 2018
%P 2607-2641
%V 20
%N 11
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.4171/jems/820/
%R 10.4171/jems/820
%F JEMS_2018_20_11_a1
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. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/820/

Cité par Sources :