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With some technical fiddling, one can define f∗ : Gp (Y ) → Gp (X) if f is projective. 1. Devissage, resolution and localization. The main theorems of the previous section have the following applications for Kp (X) and Gp (X). 2. Let i : Z → X be the inclusion of a closed subscheme, giving the full embedding of abelian categories i∗ : MZ → MX (Z). Then i∗ : Gp (Z) → Kp (MX (Z)) is an isomorphism for all p. Indeed, each coherent sheaf F supported on Z has a finite filtration with quotient sheaves OZ -modules.
A spectral sequence for motivic cohomology, preprint (1995). , Stable real cohomology of arithmetic groups. Ann. Sci. Ecole Norm. Sup. (4) 7 (1974), 235–272. , Le th´eor`em de Riemann-Roch, Bull. Soc. Math. France 86 (1958) 97-136. , Surjectivity of cycle maps, in Journ´ ees de Geom´ etrie Alg´ ebrique D’Orsay, Juillet 1992, Ast´erisque 218 (1993) 203226. , Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 2. Springer-Verlag, Berlin-New York, 1984. , The Bloch-Kato conjecture and a theorem of SuslinVoevodsky, J.
Algebraic K-theory of generalized free products. III, IV. Ann. of Math. (2) 108 (1978), no. 2, 205–256.  Wiles, A. The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131 (1990), no. 3, 493–540.