Geodesic
Réalisation $\ell$-adique des motifs triangulés géométriques. I
Documenta mathematica, Tome 12 (2007), pp. 607-671.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this work, we provide an integral $\ell$-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 $\ell$-adic realization functor. We also give a moderate $\ell$-adic realization functor in some geometrical situations.
Classification : 19E15, 19F27, 14F42
Keywords: mixed motives, $\ell$-adic realizations, algebraic cycles 
@article{DOCMA_2007__12__a1,
     author = {Ivorra, Florian},
     title = {R\'ealisation $\ell$-adique des motifs triangul\'es g\'eom\'etriques. {I}},
     journal = {Documenta mathematica},
     pages = {607--671},
     publisher = {mathdoc},
     volume = {12},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a1/}
}
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Ivorra, Florian. Réalisation $\ell$-adique des motifs triangulés géométriques. I. Documenta mathematica, Tome 12 (2007), pp. 607-671. http://geodesic.mathdoc.fr/item/DOCMA_2007__12__a1/