-adic realization of geometric triangular motives. I

  • Florian Ivorra

    Institut de Mathématiques de Jussieu Équipe Théorie des nombres 175-179 rue du Chevaleret 75013 Paris FRANCE
$\ell$-adic realization of geometric triangular motives. I cover
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In this work, we provide an integral -adic realization functor for Voevodsky's triangulated category of geometrical motives over a noetherian separated scheme. Our approach to the realization problem is to study finite correspondences from the Nisnevich and étale local point of view. We set the existence of a local decomposition for finite correspondences which implies the existence of local transfers. This result allows us to provide canonical transfers on the Godement resolution of a Nisnevich sheaf with transfers and then to carry out the construction of the -adic realization functor. We also give a moderate -adic realization functor in some geometrical situations.

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Florian Ivorra, -adic realization of geometric triangular motives. I. Doc. Math. 12 (2007), pp. 607–671

DOI 10.4171/DM/237