. Proof, By Corollary 3.2.3, the spectrum GGL S is degreewise fibrant for the projective model structure, and therefore defines an object in SH(S)

. Proof, Since f is smooth, by Corollary 3.3.9 and [Morel-Voevodsky, Proposition 3.2.9.], for any smooth Y -scheme W we have an, G X ) ? G n (W )

]. Y. Bibliographie-[-andré and . André, Une introduction aux motifs (motifs purs, motifs mixtes, périodes), Panoramas et Synthèses, 2004.

]. J. Ayoub and . Ayoub, Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique, Astérisque No, pp.314-315, 2007.

. A. Bbd, J. Be?-ilinson, P. Bernstein, and . Deligne, Faisceaux pervers, Analyse et topologie sur les espaces singuliers, I (Luminy, pp.5-171, 1981.

]. B. Blander and . Blander, Local Projective Model Structures on Simplicial Presheaves, K-Theory, vol.24, issue.3, pp.283-301, 2001.
DOI : 10.1023/A:1013302313123

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.1499

]. S. Bloch-ogus, A. Bloch, and . Ogus, Gersten's conjecture and the homology of schemes, Annales scientifiques de l'??cole normale sup??rieure, vol.7, issue.2, pp.181-201, 1974.
DOI : 10.24033/asens.1266

]. A. Borel-moore, J. C. Borel, and . Moore, Homology theory for locally compact spaces, Michigan Math, J, vol.7, pp.137-159, 1960.

]. M. Bondarko1 and . Bondarko, Weight structures vs. t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general), Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology, vol.344, issue.03, pp.387-504, 2010.
DOI : 10.1112/S0010437X06002107

]. M. Bondarko2 and . Bondarko, Weights for Relative Motives: Relation with Mixed Complexes of Sheaves, International Mathematics Research Notices, vol.2014, issue.17, pp.4715-4767
DOI : 10.1093/imrn/rnt088

]. S. Bloch and . Bloch, Algebraic cycles and higher K-theory, Adv. in Math, pp.267-304, 1986.
DOI : 10.1016/0001-8708(86)90081-2

]. Cisinski-déglise2, F. Cisinski, and . Déglise, Integral mixed motives in equal characteristic, Documenta Math. Extra Volume : Alexander S. Merkurjev's Sixtieth Birthday, pp.145-194, 2015.

[. Colliot-thélène, R. Hoobler, and B. Kahn, The Bloch-Ogus-Gabber theorem, Algebraic K-theory, pp.31-94, 1997.
DOI : 10.1090/fic/016/02

]. B. Conrad and . Conrad, Grothendieck duality and base change, Lecture Notes in Mathematics, vol.1750, 2000.
DOI : 10.1007/b75857

]. A. Corti-hanamura, M. Corti, and . Hanamura, Motivic decomposition and intersection Chow groups I, Duke Math, J, vol.103, pp.459-522, 2000.

]. F. Déglise1 and . Déglise, Coniveau filtration and mixed motives, Contemporary Mathematics, vol.571, pp.51-76, 2012.
DOI : 10.1090/conm/571/11322

]. F. Déglise2 and . Déglise, Around the Gysin triangle I, Contemporary Mathematics, vol.571, pp.77-116, 2012.
DOI : 10.1090/conm/571/11323

]. F. Déglise5 and . Déglise, Orientation theory in arithmetic geometry, 2014.

]. F. Déglise6 and . Déglise, Around the Gysin triangle II, Doc, Math, vol.13, pp.613-675, 2008.

]. F. Déglise7 and . Déglise, Modules homotopiques avec transferts et motifs génériques, thèse de Doctorat, 2002.

]. P. Deligne, . Deligne, and . Théorie-de-hodge, Th??orie de hodge, III, Publications math??matiques de l'IH??S, vol.34, issue.1, pp.5-77, 1974.
DOI : 10.1007/BF02685881

]. C. Deninger-murre, J. Deninger, and . Murre, Motivic decomposition of abelian schemes and the Fourier transform, Journal für die reine und angewandte Mathematik, vol.422, pp.201-219, 1991.

A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas (Quatrième Partie)., Inst, Hautes Études Sci. Publ. Math, p.32, 1967.

]. W. Fulton and . Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 1998.

]. R. Hartshorne and . Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard With an appendix by P. Deligne, Lecture Notes in Mathematics, vol.64, issue.20, 1963.

]. D. Hébert and . Hébert, Abstract, Compositio Mathematica, vol.3, issue.05, pp.1447-1462, 2011.
DOI : 10.2478/s11533-008-0003-2

]. P. Hirschhorn and . Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs, vol.99, 2003.
DOI : 10.1090/surv/099

]. A. Grothendieck and . Grothendieck, On the de rham cohomology of algebraic varieties, Publications math??matiques de l'IH??S, vol.VI, issue.1, pp.95-103, 1966.
DOI : 10.1007/BF02684807

]. J. Jardine and . Jardine, Motivic symmetric spectra, Doc. Math, vol.5, pp.445-553, 2000.

F. Jin, Introduction aux motifs de Voevodsky, mémoire de magistère à l'Ecole Normale Supérieure, sous la direction de Frédéric Déglise, 2012.

F. Jin, Borel-Moore motivic homology and weight structure on mixed motives, Math. Z, vol.283, issue.3, pp.1149-1183, 2016.
URL : https://hal.archives-ouvertes.fr/ensl-01411015

]. B. Kahn and . Kahn, Fonctions zêta et L de variétés et de motifs

M. Levine, Mixed motives, Mathematical Surveys and Monographs, 57, 1998.

]. M. Levine-morel and F. Levine, Algebraic cobordism, 2007.

. C. Mvw, V. Mazza, and C. Voevodsky, Lecture notes on motivic cohomology, Clay Mathematics Monographs, vol.2, 2006.

]. F. Morel-voevodsky, V. Morel, and . Voevodsky, A 1 -homotopy of schemes, Publications Mathématiques de l'IHÉS, pp.45-143, 1999.

]. A. Navarro and . Navarro, The Riemann-Roch theorem and Gysin morphism in arithmetic geometry, thèse à l, 2016.

]. Y. Nisnevich and . Nisnevich, The completely decomposed topology on schemes and associated descent spectral sequences in algebraic K-theory, in Algebraic K-theory : connections with geometry and topology, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol.279, pp.241-342, 1987.

]. D. Pauksztello and . Pauksztello, Compact corigid objects in triangulated categories and co-t-structures, Central European Journal of Mathematics, vol.6, issue.1, pp.25-42, 2008.
DOI : 10.2478/s11533-008-0003-2

URL : http://arxiv.org/abs/0705.0102

K. [. Panin, O. Pimenov, and . Röndigs, On Voevodsky's Algebraic K-Theory Spectrum, Algebraic topology, pp.279-330, 2009.

D. Quillen, Higher algebraic K-theory: I, Proc. Conf, pp.85-147, 1972.
DOI : 10.1007/BF02684591

]. J. Riou and . Riou, Op??rations sur la K-th??orie alg??brique et r??gulateurs via la th??orie homotopique des sch??mas, Comptes Rendus Mathematique, vol.344, issue.1, 2006.
DOI : 10.1016/j.crma.2006.11.011

M. Rost, Chow groups with coefficients, Doc. Math, vol.1, issue.16, pp.319-393, 1996.

A. Grothendieck, With an exposé by Michèle Raynaud. With a preface and edited by Yves Laszlo. Revised reprint of the 1968 French original, Documents Mathématiques, issue.2, 1962.

M. Artin, A. Grothendieck, and J. Verdier, Séminaire de Géométrie Algébrique du Bois-Marie Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat, Théorie des topos et cohomologie étale des schémas, pp.1972-1973, 1963.

P. Berthelot, A. Grothendieck, and L. Illusie, Théorie des intersections et théorème de Riemann-Roch, Séminaire de Géométrie Algébrique du Bois-Marie, 1966.

]. A. Suslin-voevodsky1, V. Suslin, and . Voevodsky, Bloch-Kato conjecture and motivic cohomology with finite coefficients, in The arithmetic and geometry of algebraic cycles, NATO Sci. Ser. C Math. Phys. Sci, vol.548, pp.117-189, 1998.

]. A. Suslin-voevodsky2, V. Suslin, and . Voevodsky, Relative cycles and Chow sheaves, in Cycles, transfers, and motivic homology theories, Ann. of Math. Stud, vol.143, pp.10-86, 2000.

]. R. Thomason-trobaugh, T. Thomason, and . Trobaugh, Higher algebraic K-theory of schemes and of derived categories, The Grothendieck Festschrift, pp.247-435, 1990.

]. A. Vistoli and . Vistoli, Grothendieck topologies, fibered categories and descent theory, in Fundamental Algebraic Geometry, Mathematical Surveys and Monographs, vol.123, 2006.

]. V. Voevodsky1 and . Voevodsky, Triangulated categories of motives over a field, in Cycles, transfers , and motivic homology theories, Ann. of Math. Stud, vol.143, pp.188-238, 2000.

]. V. Voevodsky2 and . Voevodsky, Cohomological theory of presheaves with transfers, in Cycles, transfers, and motivic homology theories, Ann. of Math. Stud, vol.143, pp.87-137, 2000.

]. V. Voevodsky3 and . Voevodsky, A 1 -homotopy theory, ICM 1998(I), pp.417-442

]. F. Waldhausen and . Waldhausen, Algebraic K-theory of spaces, in Algebraic and geometric topology, N.J. Lecture Notes in Math, pp.318-419, 1126.