Modules homotopiques avec transferts et motifs génériques (french), by F. Déglise

This is the original text of the author's thesis, defended December 18, 2002.

The main result of the thesis is the construction of an equivalence of category between Rost cycles modules over a perfect field k and an unstable version of the category of homotopy invariant sheaves with transfers over k (the latter was introduced by Voevodsky). Meanwhile the construction of the first arrow of the equivalence has been published separately in Mathematische Zeitschrift, volume 252, number 2.

An important consequence of this equivalence is a new proof of Voevodsky's theorem on the homotopy invariance of the cohomology of a homotopy invariant sheaf with transfers over a perfect field.

In order to show the independance of our proof with that of Voevodsky, we had to establish separately all the basic facts about sheaves with transfers. This is done over a regular base of equal characteristic. Since the defense of the thesis, it was possible to remove this latter hypothesis. This new work on finite correspondances over a regular base can be found in a separate preprint K-theory preprint archive 0765.


F. Déglise <deglise@math.univ-paris13.fr>