Unformatted text preview: sociated to the "Hodge" filtration (2.4.0.5) F j C ~176 = ~ C'({V~}, Ob/s(1Og D)), b>=j gives the usual Hodge ~ De Rham spectral sequence: (2.4.0.6) E~ "b = Rbf, (f~x/s(log D)). The second spectral sequence of this bicomplex, the one associated to the "conjugate" filtration (2.4.0.7) F k C"= Z Ca({V~} , Q~/s(l~ D)) a>k gives rise to a spectral sequence (2.4.0.8) E~'b=/~({V~}, ~sh~,(f2]/s(1Og D)))~ Ra+bf,(f2]/s(logD)) of quasicoherent d~smodules (~ denoting the quasicoherent sheaf associated to a F(S, (.0s)module), which maps canonically to the conjugate spectral sequence (2.4.0.1), (2.4.0.9) E~2'b=Raf,(~t~ ) ~ Ra+bf,(Q~/s(logD)). Of course, for each affine open coveting of X, the spectral sequence (2.4.0.8) is a spectral sequence of quasicoherent (gsmodules, but the canonical mapping from (2.4.0.9) need not be an isomorphism, even if we replace (2.4,0.8) by its direct limit over all affine open coverings of X....
View
Full Document
 Fall '11
 NormanKatz
 Sheaf, Hodge, Homological algebra, De Rham, spectral sequence, 2.4.0.2

Click to edit the document details