The dual of Brown representability for some derived categories
Abstract
Consider a complete abelian category which has an injective cogenerator. If its derived category is leftcomplete we show that the dual of this derived category satisfies Brown representability. In particular this is true for the derived category of an abelian AB$4^*$$n$ category, for the derived category of quasicoherent sheaves over a nice enough scheme (including the projective finitely dimensional space) and for the full subcategory of derived category of all sheaves over an algebraic stack consisting from complexes with quasicoherent cohomology.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.6028
 Bibcode:
 2013arXiv1305.6028C
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry;
 18E30;
 16D90;
 14F05;
 55U35
 EPrint:
 First version: preliminary version, comments are welcome! Second version: An (important) error was removed, some details were added. Comments are also welcome! Third version: a new application is added, some typos are removed. Fourth version: final version, some important corrections are made, to appear in Arkiv Math