On purity and applications to coderived and singularity categories
Abstract
Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of compact objects is none other than D^b(fp G). If G admits a generating set of finitely presentable objects of finite projective dimension, then also the derived category of G is compactly generated and Krause's recollement exists. Our main tools are (a) model theoretic techniques and (b) a systematic study of the pure derived category of an additive finitely accessible category.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.1615
 Bibcode:
 2014arXiv1412.1615S
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Rings and Algebras;
 Mathematics  Representation Theory;
 18E30 (Primary);
 14F05;
 16B70;
 16E65;
 55U35 (Secondary)
 EPrint:
 45 pages