Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

Local and stable homological algebra in Grothendieck abelian categories

Pages: 219 – 260

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n1.a11


Denis-Charles Cisinski (LAGA, CNRS (UMR 7539), Université Paris 13, Villetaneuse, France)

Frédéric Déglise (LAGA, CNRS (UMR 7539), Université Paris 13, Villetaneuse, France)


We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect to tensor products and stabilization. This gives convenient tools to construct and understand triangulated categories of motives.


stable model categories, Grothendieck abelian categories, derived functors, motivic complexes

2010 Mathematics Subject Classification

14F42, 18E15, 18G35, 18G55

Published 1 January 2009