Unformatted text preview: (4.0.1.5) wE;"'k+"= HkR"(Di, n'"nDi./S)~ Rkf.(t2;x./s(logD)). il <'"<in (4.0.2) Proposition. The spectral sequence (4.0.1.5) is (naturally) a spectral sequence with cupproduct in the category of quasicoherent (gsmodules with integrable connection relative to T. This connection is the GaussMartin connection on the El terms and on the abutment. In particular, the W filtration on the Rkf,(Q}/s(logD)) is horizontal for the GaussManin connection. Proof. The product structure in the spectral sequence results from (4.0.1.1). The action of the GaussManin connection on the spectral sequence may be seen directly as follows. The question being local on S, we may suppose S affine. Choose an affine open covering of X by suf ficiently small coordinatized open sets V v as in (3.4.1). The filtration W of f2~/s(logD) induces a filtration W on the Cech bicomplex of quasicoherent (gsmodules (4.0.2.0) W~ C~ t2}/s(logD)) dN,, C~ W~f21/s(logO) )...
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This note was uploaded on 12/21/2011 for the course MAP 4341 taught by Professor Normankatz during the Fall '11 term at UNF.
 Fall '11
 NormanKatz

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