Quelques compléments sur les modules de cycles, by Frederic Deglise

In this paper, we give some complementary constructions for Chow groups with coefficients in a cycle module defined by M.Rost. That is, we define a pullback for a local complete intersection morphism and a refined Gysin homorphism for a pullback of a regular closed immersion. We prove associativity for the pullback and a general projection formula. We obtain from this extension the existence of transfers on Chow groups with coefficients, thus proving that the unramified part defines a homotopy invariant sheaf with transfers in the sense of V. Voevodsky. This is the first step in a general comparison between the theory of cycle modules and the theory of homotopy invariant sheaves with transfers already obtained in the thesis of the author (cf. http://www-math.univ-paris13.fr/~deglise/these.html).

This preprint has been accepted for publication, and will appear in the following form.

           Title: Transferts sur les groupes de Chow à coefficients
         Journal: Mathematische Zeitschrift
       Publisher: Springer-Verlag GmbH
            ISSN: 0025-5874 (Paper) 1432-1823 (Online)
             DOI: 10.1007/s00209-005-0855-0
           Issue: Volume 252, Number 2
            Date: February 2006
           Pages: 315 - 343


Frederic Deglise <deglise@math.univ-paris13.fr>