(C) sm /S) which is by definition given by -for U/S a smooth morphism ,
, (C)/S) is by definition a natural extension of
Denote h 12 : U 12 := U 1 × S U 2 ? S and p 112 : U 1 × S U 2 ? U 1 ,
, ) are usu local equivalence by proposition 10, ? since h : U ? S is a smooth morphism, the inclusion ? U/S : h * O S ? ? ? U/S is a quasi-isomorphism, ? since h ? : U T ? T is a smooth morphism
S I ?? S the open embedding. Let i i : S i ??S i closed embeddings ,
,
,
,
Let i i : S i ??S i closed embeddings, withS i ? SmVar(C), ) sm /S) ,
,
,
,
,
,
,
,
AnSp(C) sm /S an ) ,
T an )) ? D D(1,0)f il,? (T an /(Y an × S an I )), see definition 122 and definition 143 commutes g * mod Hdg, the following diagram in ? T (D(M HM ,
, we define the Betti realization functor as
, S cw ) * Cw * S M = e(S cw ) * sing I * Cw et)(F )
, For the Corti-Hanamura weight structure on DA ? (S), we have by functoriality of (i) the functor
Note that, by considering the explicit D 1 S local model for presheaves on AnSp(C) sm /S an ,
S an ) ; by considering the explicit I 1 S local model for presheaves on CW sm /S cw ,
,
Definition 153, We have, for M ? DA(S), (F, W ) ? C f il (Var(C) sm /S) such that (M, W ) = D(A 1 , et)(F, W ), and an equivalence (A 1 , et) local e : f * (F, W ) ? (F ? , W ) with (F ? , W ) ? C f il (Var(C) sm /S) such that (f * M, W ) = D ,
,
,
,
,
,
,
,
,
, AnS *
,
,
, C f il (Var(C) sm /S) is such that (M, W ) = D(A 1 , et)(F, W )
, S )) is the isomorphism of theorem 23
,
, Gr 12
W ))) ? q is an equivalence (A 1 , et) local by lemma 5 ,
, M ) : (F DR S (M )) an ? ? ? F DR S,an (M ) is an isomorphism by theorem 41
Note sur les opérations de Grothendieck et la realisation de Betti, Journal of the Institute of Mathematics of Jussieu, vol.9, issue.02, pp.225-263, 2010. ,
L'algebre de Hopf et le groupe de Galois motiviques d'un corps de caractéristique nulle I, Journal die reine (Crelles Journal), vol.2014, issue.693, pp.1-149 ,
L'algebre de Hopf et le groupe de Galois motiviques d'un corps de caractéristique nulle II, Journal die reine (Crelles Journal), vol.2014, issue.693, pp.151-126 ,
Les six opérations de Grothendieck et le formalisme des cyclesévanescents dans le monde motivique I et II, Société de Mathématiques de France, Astérisque, vol.314, 2006. ,
On the derived category of perverse sheaves, in K-theory, arithmetic and geometry, Lecture Notes in Mathematics, vol.1289, pp.27-41, 1987. ,
Weight structure vs. t-structure ; weight filtrations, spectral sequences, and complexes (for motives and in general), Journal of K-theory, vol.6, issue.3, pp.387-504, 2010. ,
On the realization functor of the derived category of mixed motives ,
On the V-filtration of D-modules in algebra and number theory, Progr, Math, vol.235, pp.59-70, 2005. ,
, Homotopy theory of mixed Hodge Complexes, 2013.
Triangulated categories of mixed motived ,
Motivic decomposition and intersection Chow groups I, Duke math, J, vol.103, pp.459-522, 2000. ,
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
On the De Rham cohomology of algebraic varieties, Inst. Hautes Etudes Sci. Publ. Maths, vol.45, pp.5-99, 1975. ,
Algebraic Topology, 2002. ,
Resolution of singularities of an algebraic variety over a field of caracteristic zero, Ann. of Math, vol.79, pp.205-326, 1964. ,
, Perverse Sheaves, and Representation Theory, 2008.
Perverse, Hodge and motivic realization of etale motives, Compos. Math, vol.152, issue.6, pp.1237-1285, 2016. ,
The Riemann-Hilbert problem for holonomic systems, Publications of the Research Institute for Mathematical Sciences, vol.20, issue.2, pp.319-365, 1984. ,
, Sheaves on manifolds, 1990.
Réalisation de Hodge des motifs de Voevodsky, manuscripta mathematica, vol.141, pp.663-697, 2012. ,
Transformations canoniques et specialisation pour les V-modules filtrés ,
Homotopy limits in triangulated categories, Compos. Math, vol.86, pp.209-234, 1993. ,
Mixed motives, Handbook of K-theory, vol.1, pp.429-521, 2005. ,
Mixed Hodge Structures, vol.52, 2008. ,
, Singularités des systemes differentiels de Gauss-Manin, vol.2, 1979.
, Lecture notes on motivic cohomology, vol.2, 2006.
Mixed Hodge Modules, Proc. Japan Acad. Ser, A.Math.Sci, vol.62, issue.9, pp.360-363, 1986. ,
Géometrie algébrique et géometrie analytique, Annales de l'institut Fourier, vol.6, pp.1-42 ,
Dualité dans la cohomologie des espaces localement compacts, Seminaire Bourbaki, vol.9, pp.337-349, 1995. ,
Des categories dérivées de catgories abéliennes, Asterique, vol.239, 1996. ,
,
,