Modules homotopiques

Abstract

Based on previous works, we compare over a perfect field $k$ the category of homotopy invariant sheaves with transfers introduced by V. Voevodsky and the category of cycle modules introduced by M. Rost: the former is a full subcategory of the latter. Using the recent construction by D.C. Cisinski and the author of a non effective version $DM(k)$ of the category of motivic complexes, we show that cycle modules form the heart of a natural t-structure on $DM(k)$, generalizing the homotopy t-structure on motivic complexes.