Geodesic
$\ell$-adic realization of geometric triangular motives. I
Documenta mathematica, Tome 12 (2007), pp. 607-671

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In this work, we provide an integral l-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 l-adic realization functor. We also give a moderate l-adic realization functor in some geometrical situations.
DOI : 10.4171/dm/237
Classification : 14F42, 19E15, 19F27
Mots-clés : algebraic cycles, mixed motives, l-adic realizations 
Florian Ivorra. $\ell$-adic realization of geometric triangular motives. I. Documenta mathematica, Tome 12 (2007), pp. 607-671. doi: 10.4171/dm/237
@article{10_4171_dm_237,
     author = {Florian Ivorra},
     title = {$\ell$-adic realization of geometric triangular motives. {I}},
     journal = {Documenta mathematica},
     pages = {607--671},
     year = {2007},
     volume = {12},
     doi = {10.4171/dm/237},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/237/}
}
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